Gr. 11 Physics Forces

Transcription

1 Gr. 11 Physics Forces This chart contains a complete list of the lessons and homework for Gr. 11 Physics. Please complete all the worksheets and problems listed under Homework before the next class. A set of optional online resources, lessons and videos is also listed under Homework and can easily be accessed through the links on the Syllabus found on the course webpage. You may want to bookmark or download the syllabus for frequent use. Forces 1 Interactions and Forces Idea of force, interactions Video: Fundamental Forces Assign Physics Minute Presentations Handbook: Interactions pg.4 2 What is the Effect of a Force? Force causes acceleration Video: Feynman and Inertia 3 The Force-Motion Catalogue Combining forces, net force, Newton s 1 st Law Handbook: The Net Force pg.10 Video: Inertia Hip-Hop Read: Newton s First Law of Motion, pg The Change of Force Principle Systems, inertia, changing forces Handbook: The Force-Change Principle pg.13 Lesson: First Law Video: Forces in Space! 5 The Force of Gravity Quiz: 1 st Law + Net Force Force of gravity, gravitational field strength, F g = mg Read: Gravitational Force on Earth s Surface, pg Problems: pg. 85 #2-5, pg, 86 #6-8, pg. 87 #10 Handbook: Force of Gravity Homework pg.14 Video: Big Bang Theory Video: Defining Gravity Video: Gravity Newton to Einstein 6 Normal Force Normal force Read: Forces we Experience Daily, pg Handbook: Normal Forces Homework pg.16 Lesson: Normal Force Video: Normal Force 7 Force, Mass and Motion Force and mass affect acceleration Video: Cars and Inertia 8 Force, Mass and Motion part 2 9 Newton s Second Law Problem Solving Newton s 2 nd law, F net = ma, definition of force, definition of Newton, inertia Read: Newton s Second Law of Motion, pg Problems: pg. 73 #1,2,4,6 Handbook: Force, Mass and Acceleration pg.22 Lesson: Newton s Second Law Video: 2 nd Law in Space! Force problem solving techniques Problems: finish handbook questions and pg. 81 #16 Lesson: Finding the Net Force Video: Misconceptions About Freefall 10 Interaction Forces Forces are interactions Video: 3 rd Law in Space! Video: Newton s Third Law 11 Newton s 3 rd law Newton s 3 rd Law, Force pairs Read: Newton s 3 rd Law of Motion, pg Handbook: Newton s Third Law Homework pg Friction Kinetic and static friction Read: Effects of Friction, pg Video: Brake Test 13 Friction Coefficient of friction, F f = F n Problems: pg 97 #1, pg. 100#1, pg. 103 #3,4,5,6 pg. 105#7 Lesson: Static and Kinetic Friction Lesson: Friction Problem 14 Review Problems: pg. 107 #1,2,5, pg 111 #16, pg. 114 # 13,20,22,24,25,26 Review: Newton s Laws 15 Test 1

2 SPH3U: Interactions and Forces When two objects affect one another in some way we say that they interact. Today we begin exploring the nature of these interactions and what happens as a result. Recorder: Manager: Speaker: A: Thinking About Interactions A friend of yours kicks a soccer ball which you record on video. You carefully watch the video frame by frame and think about the interactions that are present. 1. Observe. There is an interaction between the foot and the ball. In which frames is the interaction present? Reason. What evidence is there that there is an interaction between the ball and foot? Why do we believe the ball is affected in some way? Is the foot affected in some way? (Your friend would definitely notice this!) 3 4 The ball and foot interaction is an example of a contact interaction. Such an interaction is only noticeable when the two objects are in contact. When they are not in contact, there is no interaction. 3. Reason. Does the ball participate in any other contact interactions? In which frames and between which objects? Non-contact interactions can take place when the objects are not in contact. Even though the objects are separated by some distance, they still have an effect on one another. Note that an interaction always involves a pair of objects. 4. Reason. Does the ground participate in a non-contact interaction with the ball? Explain. 5. Reason. Does Earth participate in a non-contact interaction with the ball? Explain. For the purpose of understanding interactions, we will think of and describe the ground and Earth as two separate objects since they often participate in interactions in different ways. We can construct an interaction diagram (ID) to help represent the interactions present at some moment in time. An ID lists all the objects that are interacting with one another and has lines representing each interaction. The lines are labelled with a single letter describing the type of interaction: a = applied (a person s contact), g = gravitational, n = normal (surfaces in contact) and many more! There can be many, many interactions in a given situation so we need to narrow our focus by selecting a system: an object or collection of objects whose interactions we are interested in. We show the system objects by drawing a circle around them. We will usually leave out other interactions that don t involve the system objects. 2

3 6. Represent. In the chart below, complete the interaction diagrams for each of the four frames of the video ball n g ground Earth B: A Model Interaction We are going to use an elastic band to examine an elastic interaction. Each member of your group should try this. You will need two identical elastics. 1. Describe. Loop one elastic band around your two pointer fingers. Separate your fingers until the elastic band has a bit of stretch. Use a ruler to help ensure a consistent amount of stretch. Describe the effect the elastic has on each finger. 2. Represent. How does the pull of the elastic on each finger compare? Draw an arrow representing the force due to the elastic that each finger experiences. The arrow should start from each finger on the diagram. (Don t draw the elastic.) Every interaction has two parts called forces. Intuitively, a force is a push or a pull of one object on another. In our previous example, we say the two fingers are interacting with one another through the elastic. The fingers pull on each other. 3. Describe and Represent. Rest your fingers and try again using two elastics stretched to the same distance you measured before. Describe how the sensation of force on your fingers has changed. Draw arrows again and explain how you chose to draw their length. 4. Reason. What type of quantity best represents a force: scalar or vector? Explain. C: Measuring Force We will use a spring scale to measure the size of forces. First you need to calibrate the spring scale. Hold the scale horizontally or vertically just as you will use it when measuring, but without pulling on the hook. Adjust the scale (a sliding cover or nut at the top) so it reads zero. The scale reads in units called newtons whose symbol is N. In physics we simplify the real world in order to focus on the basic ideas. Instead of drawing a beautiful diagram of a hand each time, we will represent the hand using a model. In grade 11 we will model all our objects as a point particle: we imagine all the mass of the object compressed into a single point. The diagram we create is called a force diagram. 1. Represent. Create your elastic interaction like in B#1, but replace one finger with a spring scale. What is the size of the force in this interaction? Draw an arrow starting at the dot that represents your finger. Label the size and direction of the force on your finger (for example, 3.1 N [left]). Force Diagram 2. Predict and Test. You will replace your second finger with a second spring scale and hold the elastic to its consistent length, what will each scale read? Explain your prediction. Test it. 3

4 SPH3U Homework: Interactions Name: A: Interactions and Forces There are many different ways in which objects can interact and these different types of interactions can be organized into two large groups. Some common ones are listed below. Types of Interactions / Forces Tension (t) = two objects pulling on each other through a rope or string (no stretching) interactions Elastic (e) = two objects push/pull on each other due to stretch or compression of material Friction (f) = resistance between two surfaces that are slipping or trying to slip past each other contact non-contact Normal (n) = two surfaces in contact and pressing in to each other tension friction normal gravitational magnetic Applied (a) = the contact force due to a person a combination of friction and normal forces elastic applied Gravitational (g) = the gravitational interaction between two objects Magnetic (m) = the magnetic interaction between two objects 1. Represent. For each situation below complete the missing parts: the description (with the system), the sketch, or the interaction diagram. Situation 1 Situation 2 Situation 3 Situation 4 You pull a ball upwards using a string. system = ball system = rock system = metal bar system = hand t f sidewalk wagon g n Earth 2. Reason. In situation #2 above, your described the interactions for a rock being lifted up. How many interactions are there between the hand and the rock? Often we describe the person s interaction as applied. In this situation, what type of interaction is it really? (Look at the chart above for a hint). Explain. 3. Represent. Draw a force diagram for situation #1 above. Describe how you chose to draw the force vectors. 4

5 SPH3U: What is the Effect of a Force? What happens when a single force acts on an object? This is a tricky question that took very clever people about 2000 years to figure out. Now it s your turn! (Don t worry - it won t take as long this time around.) In all the examples that follow, we will be examining the effect of a single, constant force. Recorder: Manager: Speaker: A: The Steady Pull 1. Prediction. How do you think the dynamics cart will move when you exert a constant horizontal force (a steady push or pull) on it? 2. Design. You need a dynamics cart, some masses, one elastic band and a ruler. Test and describe a technique that will allow you to exert a constant force (how did you do this last class?) on the dynamics cart using these materials. You should be able to do this for an interval of about four seconds (this is why the masses are helpful). Take your time doing this. 3. Reason. To achieve a constant force, what must you observe about your elastic? *** Practice your technique until you are good at it! Demonstrate this for your teacher before going on. *** 4. Represent. Draw an interaction diagram for the system of the cart while you are exerting the constant force. ID 5. Prediction. If necessary, revise your prediction from question A#1 based on what you have already observed. Use a dashed line to show what the velocity graph and motion diagram might look like. 6. Test. (as a class) Once you are very confident in your pulling technique, pull the cart on the track in front of the motion detector. Describe how your predictions compare with the computer results. Make any changes necessary to the diagrams above. v t B: Release the Cart! Pull the cart along the floor at a constant speed and then release it. 1. Observe. Describe the motion of the cart after it has been released. 2. Represent. Complete the motion graphs and diagrams on the next page. Label two events on each: (1) the cart is released, and (2) the cart comes to rest. 5

6 3. Test. (as a class) Use the cart on the track with the motion detector to verify your graphs above. Describe any differences you noticed. v +x t 4. Reason. Emmy says, I think the cart slows down as the initial push runs out. I don t see anything pushing or pulling on it after we let go which means no forces. Marie says, I bet there is a force causing it to slow down. I have evidence for this interaction rub your hands together quickly and feel. Who do you agree with? Explain. 5. Reason and Represent. Imagine we could change the cart and floor to reduce friction a bit. Explain how the motion of the cart after it is released would be different. Sketch a velocity graph for this imaginary situation and explain how it appears different from the previous velocity graph. v t 6. Reason and Represent. Now imagine we very carefully remove all sources of friction. After we release the cart, what would we observe in this very special situation? Sketch a velocity graph. In this situation what horizontal forces are acting on the cart? v t C: Starting the Force-Motion Catalogue 1. Reason. Describe the motion that results from an object experiencing the two situations listed in the chart below. This will start our catalogue of force-motion relationships. Situation One single, constant force No forces at all (two possibilities!) Resulting Motion 1) 2) 2. Reason. Isaac says, Wait a minute in reality, our cart experiences a little friction all the time. But we said there was only one force acting on it while it sped up - the one from our elastic. This means our conclusions about the effects of a single force might be wrong. Do you agree or disagree with Isaac? Do you think our conclusions might be different if friction was completely zero? Explain. 6

7 SPH3U: The Force-Motion Catalogue A car driving down the road experiences many forces at the same time. What happens in such a case? In this activity you will find out. You will need: a dynamics cart and two identical spring scales (5 or 10 N). Throughout this activity friction is very small compared to the other forces involved and therefore its effects can be ignored. Recorder: Manager: Speaker: A: Two Forces Exert two equal forces on the cart, but in opposite directions. 1. Observe. Describe the motion of the cart. Record the size of the forces. Spring scale + y + x Spring scale 2. Represent. Draw a force diagram () showing the horizontal forces only (just for today!). Label the forces (for example, F1 3N[ right ] ) The net force (F net ) is the combined effect of all the forces acting on an object or system. Since there may be forces in more than one direction (horizontal and vertical) we will often describe the forces and the net force in a particular direction (F net x or F net y ). 3. Reason. Without doing any math, what do you think the net force experienced by the cart in the x-direction equal to? To calculate the net force we will write a scalar equation using a sign convention to show directions. Forces acting in the positive direction are labelled positive and forces acting in the negative direction are labelled negative. The values of the force symbols are all positive. For example, if there is a single 10-N force in the negative x-direction, we will write: F net x = - F 1, where F 1 = 10 N. 4. Calculate. Which force on your force diagram above is in the positive x-direction? Which is in the negative x-direction? Complete a scalar equation for the net force experienced by the cart in the x-direction using the symbols F 1 and F 2. Be sure to by writing a positive or negative sign in front of the force symbol. Then substitute values for the forces and complete the calculation. F net x = ** Check your results with your teacher before continuing** In the future, if the first symbol in the expression for the net force is positive, we won t write the positive sign. If the net force equals zero we say that the forces acting on the object are balanced. In part A, the forces acting on the object in the x- direction are balanced. B: Net Force Zero Double Attwood Machine The example in Part A demonstrated that an object initially at rest that experiences a net force of zero will remain at rest. What will happen to an object that is already moving which experiences balanced forces? 1. Represent. Draw a for the cart your teacher has set up. Label the two forces. Note that the strings attached to the weights are pulling on the cart horizontally. Use the force values your teacher gives you. 2. Calculate. Write an expression for the net force in the x-direction and calculate the result. 7

8 3. Prediction. Your teacher will start the cart moving and then let go. Once released, the only horizontal forces acting on the cart will be those provided by the strings. How do you think the cart will move after being released? 4. Test. (as a class) Describe your observations. Do they confirm your prediction? Explain. C: Net Force is Not Zero This is another class demonstration. The only difference with the previous one is that one of the weights is a little bit larger. 1. Represent. Draw a and label the two forces. Use the values your teacher gives you. 2. Calculate. Write an expression for the net force and calculate the result. If the net force is not equal to zero, we say that the forces acting on the object are unbalanced. 3. Prediction. How will the car move after it is released? 4. Test. (as a class) Describe your observations. Do they confirm your prediction? Explain. If a system accelerates, draw a separate wiggly acceleration vector ( a ) alongside the force diagram. 5. Predict. According to your calculation for the net force, what single force could replace the two forces in this situation? Draw a for this situation. How does it compare with the previous? 6. Test. (as a class) The cart now experiences a single force equal to the net force from before. How does the motion of the cart compare with your previous observations? The net force gives us the combined effect of all the forces acting on an object. The object behaves just as if a single force was acting on it that had the same magnitude and direction as the net force. Judging from only the motion of the object, we cannot tell the difference. We will call this idea the net force principle. 7. Predict. We haven t thought carefully about what forces may be acting on the cart in the vertical direction. Use your new understanding of net forces and the vertical motion of the cart. What do you think the net force in the vertical direction is equal to? Is there any evidence for a force other than gravity acting in a vertical direction? Explain. 8

9 8. Predict. Let s suppose that the cart experiences a force of gravity of 9 N downwards. What can you predict about the size and direction of the other vertical force? What interaction do you think it comes from? When two objects are in contact, they interact and exert normal forces (F n ) on one another. You have just correctly predicted the existence of this force! We will learn more about this force later. D: Three Forces! It is now time to return to your dynamics cart. Your challenge is to create a situation where three forces in the x-direction are balanced. 1. Reason and Represent. Decide how you will attach the spring scales and draw a. Label the forces. 2. Calculate. Write an expression for the net force and use your values to calculate the result. 3. Reason. Explain why you think you succeeded in this challenge. E: Completing the Forces-Motion Catalogue Complete the catalogue below showing the force and motion relationships based on your observations thus far in this unit. Situation Net Force Resulting Motion (circle one) No forces at all zero / non-zero 1) 2) Balanced forces (two or more) One single, unbalanced force Unbalanced forces (two or more) zero / non-zero 1) 2) zero / non-zero zero / non-zero 1. Reason. Which situations above produce the same kinds of motion? What property do they have in common? 2. Summarize. Devise a rule that relates the net force with the resulting motion. 9

10 SPH3U: The Net Force Homework Name: 1. For each force diagram, decide if the forces appear to be balanced or unbalanced. Write the expression for the net force in the x- or y-direction. Use the directions right or up as positive. What type of motion will be the result: acceleration or rest/constant velocity? Look at the sample answers for hints on what to do if you re stuck. a f a t n a a t f Balanced? unbalanced F net x = F f F a Motion? positive acceleration t n n a g g tg g Balanced? balanced F net y = F n - F g Motion? negative acceleration 2. Two forces act in opposite directions on an object, F R to the right and F L to the left. Indicate the direction of the acceleration with a wiggly acceleration vector. Compare the size of the two forces. Draw a force diagram. Motion Diagram 2 1 Accel. Compare F L > F R Force Diagram L R 3. Each situation is described by a force diagram and an initial velocity. Draw a motion diagram for each situation. You may assume that the object does not change direction. v 1 0 negative positive Motion Diagram t f a t a 1 2 t n a 10

11 SPH3U: The Change of Force Principle We have made a great discovery with Newton s First Law (our catalogue of forcemotion relationships). Our next task is to figure out what happens to the motion when forces change. Recorder: Manager: Speaker: A: Systems and Interactions Your teacher has a cart set up on a track with a motion detector and a force sensor. The cart glides very smoothly along the track so the force of friction is small enough to ignore. Our experiment has three events: (1) the cart is released from rest and the counterweight pulls on it, (2) the counterweight hits the ground, and (3) the cart reaches the end of the track. A system is the object or collection of objects we are interested in studying. At our level of physics, we will think of the system as a single object with the combined mass of all the objects inside. The environment is composed of the other objects outside of the system which interact with the system. 1. Interpret. Examine the interaction diagram shown below. Does this diagram correspond to the interval between events 1 and 2, or between events 2 and 3? Explain. Interaction Diagram 2. Represent. Complete the force diagram for the system of the cart and masses. Describe which forces you chose to draw and why. Draw your on your whiteboard to share with the class. track g earth n cart n t weights counter -weight Force Diagram Force diagrams only show external forces - the forces from interactions between system objects and the environment. They do not show internal forces, forces from interactions between the system objects. B: Force and Motion Changes Let s return to our experiment. 1. Predict. Complete the graph showing your prediction for the velocity of the cart during the experiment. Use a dashed line. Label the three events. Interval Velocity v 2. Test. (as a class) Observe the results from the computer. Record the readings for the force probe showing the tension force. 3. Represent. Draw a for the system during each time interval. Include a wiggly acceleration vector where appropriate. Write a scalar equation for the net force during each interval. Tension force F t t t 4. Observe. What do you notice about the moments in time when the acceleration changes and when the tension force changes? F net x 11

12 5. Reason. Isaac says, When the counterweight stops pulling on the cart, the cart continues to move with a constant velocity because the cart carries the pulling force with it. I think we should draw a forwards force on the between events 2 and 3. Do you agree or disagree with Isaac? Explain. C: Throw in the Towel Now we will repeat this experiment with just one change a piece of paper towel is taped underneath the cart such that it rubs on the track as the cart moves. 1. Observe and Predict. (as a class) Watch as your teacher performs the experiment without collecting data. Draw your prediction for what you think the velocity and force graphs will look like. 2. Test. (as a class) Watch a second time with the computer readings and compare your predictions with the data. Interval Velocity Tension force v F t t 3. Represent. Draw a for the cart for the two intervals. Write an expression for F net x. 4. Observe. What do you notice about the moments in time when the acceleration changes and when the force changes? t F net x When the net force experienced by a system changes, the acceleration changes at the same time. There is no delay between one and the other. We will call this idea the change of force principle. 5. Reason. Isaac had predicted that the velocity graph for part C looks like the one shown to the right. What thinking led Isaac to predict this? Explain. All matter has a property called inertia. When forces are unbalanced, it takes time for the velocity of an object to change. In some cases the time interval can be very small, but it is never zero. We will call this idea the inertia principle. The amount of time is related to the size of the net force and the amount of inertia (the mass). 6. Reason. Albert says, When I push a box along the floor and let go it suddenly stops. Do you agree with Albert? Explain. 12

13 SPH3U Homework: The Force-Change Principle Name: A: The Falling Rock Consider the situation shown to the right of a falling rock. 1. Represent. Draw an interaction diagram (ID) for the falling rock. The Air Resistance Rule: For our purposes, we will always assume there is no air resistance (F air ) unless it is mentioned in the problem or the situation does not make sense without it. 2. Represent. Draw the for the rock while it is falling. Show your choice of sign convention. Always include an acceleration vector when appropriate. 3. Represent. Write an expression for the net force in the y-direction. ID B: The Rock Toss A rock is tossed straight upwards. It is released from the hand and is still travelling upwards. 1. Represent. Draw an ID and a for the rock while it is moving upwards. 2. Represent. Write an expression for the net force in the y-direction. ID 3. Reason. Isaac says, How can something be travelling upwards when the only force acting on it is downwards? There must be an upwards force acting on the rock. Do you agree or disagree? Explain. 4. Reason. Examine the two force diagrams for the two situations above. Explain what we cannot tell from a force diagram. Motion Diagram ID C: The Skateboard Your friend is standing on a skateboard. In order to get her started, you push and then let go as she glides away. ID Represent. Draw a motion diagram for this situation. Then draw an ID and for each interval of the trip. Describe and label any important events. 13

14 SPH3U: Force of Gravity Homework A: Where Are We? The size of the force of gravity depends on the mass of the object (m) and the strength of the gravitational field at object s location (g). Complete the chart below. Assume your mass is kg. Force of Gravity N N Location Moon Toronto Location g (N/kg) Toronto Mt. Everest Moon Alert, Nunavut B: Representing Forces Complete the chart for each situation described. Description Sketch Interaction Diagram Force Diagram Net Force 1 A cart glides along a table with no friction. A weight rests on top v F net x = of the cart. System = cart+weight F net y = 2 A tasty chocolate in your hand is moving upwards with a constant speed. v System = chocolate 3 You pull upwards on a heavy dumbbell, but it doesn t move. System = dumbbell 4 You pull along the horizontal handle of a wagon. It travels along the rough ground and speeds up. v System = wagon 5 You lower a ball using a string with a constant speed. System = ball 14

15 SPH3U: The Force of Gravity! How does an object s mass affect the size of the force of gravity it experiences? Let s find out. You will need: one 10-N spring scale, a hanging mass, a variety of masses, and some gravity. Recorder: Manager: Speaker: A force that is noticeable only when two objects are in contact, is a contact force. Any force that has a noticeable effect even when the objects are separated is called a non-contact force. 1. Reason. Is gravity a contact force or a non-contact force? How can we tell? 2. Represent. Draw an ID and a for the hanging mass. Explain why we can use the scale reading (an upwards force of tension) to determine the size of the force of gravity. ID 3. Design. We want to find out how the magnitude of the force of gravity depends on the mass of the object. Describe how you will conduct a simple experiment to collect data and determine this. 4. Observe. Record your data in the chart. 5. Analyze. Decide which variable is the dependent one. Check with your teacher. Plot your data on the graph. Use the shape of the graph to describe how the force depends on the mass. 6. Calculate. Determine the slope of your graph, including units. Show your work on the graph. Mass (kg) 0 Force of Gravity (N) The slope of your graph gives a very important quantity, the gravitational field strength g. It tells us how much force the earth s gravity exerts on each kilogram of matter in an object. The exact value depends on many factors including geographic location, altitude, and planet. The accepted value for your location is: N/kg [down]. This quantity should not be confused with the freefall acceleration: a f = 9.80 m/s 2. They may look similar, but they have different meanings. 7. Analyze. Write an equation for your line of best fit use the symbols F g and m. 8. Apply. Use your new equation to determine the size of the force of gravity acting on a 1.5x10 3 kg car. 15

16 SPH3U: Normal Forces Homework Name: You grab your physics textbook off a shelf and lower it down on to your desk in preparation for doing your homework. (What a good student you are!) As the book moves, it lies flat on the palm of your hand. Let s take a look at the physics of this daily routine. There are four important events that take place: (1) The book begins to speed up as it starts moving downwards, (2) the book reaches a constant velocity, (3) the book begins to slow down as it nears the desk, and (4) the book comes to rest at the bottom. ID 1. Represent. Draw an interaction diagram for the system of the book during this sequence of events. 2. Represent. Complete the chart below for each of the three intervals in the book s downwards motion. 3. Explain. Which force changes during this sequence of events? How does that affect the book s motion? 4. Calculate. The mass of the book is 1.3 kg. What is the size of the force exerted by your hand between events 2 and 3? Interval Motion Diagram +y +y +y 5. Test and Describe. Try this. Find a heavy book and place it on the palm of your hand just like in the picture. Lower the book just as we have described above. Try to connect how it feels in your hand when you do this with your understanding of the forces. Describe what you notice. Force Diagram Net Force = = = 7. Reason. Your friend places the same book on a table. She then leans on top of it, pushing down with 7 N of force. Draw a for book with and without the downwards push. Compare the size of all the forces in the two diagrams. no push push 8. Represent. You throw a very bouncy ball which hits a wall and then the ceiling. Draw an ID and a for the ball while it is (a) in contact with the wall and (b) in contact with the ceiling. Hint: the direction of the acceleration vector is tricky just make a guess based on the. Sketch ID Sketch ID 16

17 SPH3U: The Normal Force A: A Mysterious Force Your friend places her backpack on a table. The backpack is the system. 1. Reason. Your friend draws a for the system and says, I m really not sure that there should be an upwards force. Convince your friend. Cite direct evidence about the system that you can readily observe. Recorder: Manager: Speaker: ID g 2. Reason. Complete her original and draw an ID. The backpack has a mass of 5.8 kg (all those textbooks). What is the size of the upwards force? When two objects press against one another, they interact and exert normal forces on one another. A normal force (F n ) is a contact force that is always perpendicular to the surfaces at the point of contact. This force usually prevents objects from deforming by much, from breaking or from merging together. When a person is in contact with another object, we call this special normal force an applied force. Note that an applied force can also be a combination of a normal force and a friction force (which we will study later). B: Evidence for the Normal Force For these activities you need two metre sticks, a spring scale and a 500 g mass. Make a bridge using the metre stick between two tables. Gently press downwards with your finger in the middle of the metre stick. 1. Observe. Describe what you observe happening to the rigid metre stick. Why did the shape change? 2. Reason. Describe the evidence you feel for the existence of an upwards force acting on your finger. 3. Observe. Place the 500 g mass on the metre stick. Describe what happens. What is the size of the upwards normal force? 4. Observe. Remove the mass. Place the second metre stick directly on top of the first (the table is now twice as thick). Place the 500 g mass on top of the two sticks. What is different about the effect of the mass on our thicker table? How has the upwards normal force changed? Explain. ** Check with your teacher before proceeding. ** 17

18 5. Reason. Imagine many, many metre sticks stacked up (a very thick table). What would happen to the metre sticks if we place the 500 g mass on top of them? How has the size of the upwards normal force changed compared to the single metre stick situation? Explain. 6. Reason. We are using the metre sticks to model the surface of a solid object. What is happening inside any object that is in contact with another in order to produce normal forces? Make a guess and quickly move on. C: Measuring the Normal Force You need a 0.5kg mass and a 10 N spring scale. Rest your hand on the table and place the mass on the flat palm of your hand. 1. Reason. What is the size of the upwards normal force on the mass? Explain. 2. Predict and Calculate. Another member of your group will pull upwards on the mass with a 3 N force. Draw an ID and a for this situation. What do you think will happen? How do you think your hand will feel? What will the size of the normal force be? Explain. ID 3. Test. Attach a spring scale to the mass and exert a 3 N force upwards. How did the sensation in your hand change? What force or forces do you think have changed size when the upwards was added? The magnitude of the normal force depends on how hard the objects are pressing against one another. Other forces and motion may affect the size of a normal force. As a result, we always have to find the size of the normal force by analyzing what s happening to the system. 18

19 SPH3U: Force, Mass and Motion What factors affect the acceleration of an object? We have already hinted that force and mass are key. Today s investigation will help you understand how these quantities affect the acceleration. Your group will use the carts and masses set up in the classroom. A motion detector will help track the velocity of the cart. Complete all the questions below before beginning the experiment and show this page to your teacher. m A Recorder: Manager: Speaker: Motion detector m B A: The Atwood Machine 1. Reason. Why does each mass, m A and m B, move when released. What forces cause the acceleration of each mass? 2. Reason. When the mass, m A, is released how much mass is moving in total? 3. Reason. We can think of the two masses as a single system. What single force is the ultimate cause of the motion of the entire system (m A and m B together)? This is the force we will vary in our experiment. 4. Reason. To conduct a scientific investigation one must always change only one quantity and measure the results while ensuring that everything else remains unchanged. Suppose you want to increase the force moving the system while keeping everything else the same. You add 50 g to m B. What else must you do? B: Investigating the Effects of Force In the first experiment you will vary the force while keeping all other properties constant, to determine the effect of the net force on the acceleration. The computer will produce a velocity-time graph for you to analyze. 1. Design an Experiment. Describe how you will conduct your experiment. Show your teacher when you are ready. ** check with your teacher before continuing ** 19

20 Net Force (N) 2. Observe. What is the total mass of your system (m A + m B )? Remember, you must keep this constant! 3. Observe. (as a class) Conduct the experiment and record your results in the chart below. m A (kg) m B (kg) System Mass (kg) Net Force (N) Acceleration (m/s 2 ) 4. Represent. Construct a graph of your results with the net force on the vertical axis. We are choosing the axes this way to help with the interpretation of the slope at a later step. Draw a line of best fit. 5. Interpret. Use the pattern in your graph to help explain how acceleration depends on force. 6. Calculate. Determine the slope of the line of best fit. Show your work. Acceleration (m/s 2 ) 7. Interpret. Is the value of the slope close to any other quantities which describe our system? What do you think the slope physically represents about the object? 8. Represent. Write an equation for the line on your graph. Use symbols for net force and acceleration. 9. Reason. If we double the force acting on the system, what will happen to the acceleration? 10. Reason. If we reduce the force to one third, what will happen to the acceleration? 20

21 C: The Effect of Mass on Acceleration This is a quick investigation what will help us to determine how changing the mass of the system will affect the acceleration, when the net force remains constant. 1. Design an Experiment. (As a class)we want to double the mass of the system and keep the net force constant. Choose your original values and changed values for m A and m B that will accomplish this. Keep in mind the actual mass of the cart as you do this. m A (kg) m B (kg) System Mass (kg) Net Force (N) Acceleration (m/s 2 ) Yesterday Today Today 2. Observe. Use the Atwood machine and motion detector to conduct your investigation. Record your results above. 3. Find a Pattern. Roughly speaking what happened to the value of the acceleration when you doubled the mass? 4. Reason. What do you think the acceleration would be if you were able to reduce the original system mass by one third? Explain. D: Conclusions 1. Summarize. How does a system s acceleration depend on the net force? 2. Summarize. How does a system s acceleration depend on the system mass? 3. Speculate. Create an equation that shows the relationship between the net force (F net ), the mass (m) and the acceleration (a) of a system. 21

22 SPH3U: Force, Mass and Acceleration Homework Newton s Second Law ( and effects (acceleration). F net Name: ma ) is the rule for our universe that describes the relation between cause (forces) A: The Units of Force 1. Reason and Explain. The unit of the newton (N) is actually made up from a combination of more simple units. Use the equation for the 2 nd law to find the net force experienced by a 1.0 kg mass that accelerates at 1.0 m/s 2. Use this to explain what simpler units the newton is made from. 2. Represent and Explain. A 3 kg rock is falling to the ground. (a) Draw an ID and. (b) Determine the size for the force of gravity acting on the rock. ID (c) Use Newton s second law to find the acceleration of the rock while it is falling. Explain why the units of the calculation work out to give an acceleration. B: Find the Missing Force 1. You pull your friend on a wagon using a horizontal, forwards force. There is a small amount of friction. The wagon is gradually speeding up. (a) Represent. Draw an ID and a for the system of wagon + friend. ID (b) Reason. Which horizontal force is larger? Explain. (c) Represent. Complete the expressions for the Newton s second law in the x- and y-directions. Use the symbols for the forces and a sign convention. If the acceleration in a direction is zero, substitute that in your expression. F net x = ma x F net y = ma y = = (d) Reason. The mass of your friend is 57 kg. The mass of the wagon is 12 kg. What is the mass of the system? What mass value will you substitute for m in your equation? Explain. (e) Solve. Your friend speeds up at a rate of 1.1 m/s 2. You pull with a force of 97 N. What is the size of the force of friction? 22

23 SPH3U: Force Problem Solving Forces help us to understand why things move the way they do. Newton s 2 nd Law, F net = ma, is the law of cause and effect: it relates the causes of motion (forces) with the effects (acceleration). As a result, any problem that involves both force Recorder: Manager: Speaker: and motion will likely use the 2 nd law. To understand the force side of the equation we use force diagrams and calculate the net force. To understand the acceleration side we use motion graphs and the BIG 5 equations. A: The Elevator An elevator and its load have a combined mass of 1600 kg and experience a force of gravity of N. It is initially moving downwards at 12 m/s. Find the tension in the supporting cable when the elevator is brought to rest with a constant acceleration in a distance of 42 m. Complete the parts of our solution process below. A: Pictorial Representation Sketch, coordinate system, label givens & unknowns with symbols, conversions, describe events B: Physics Representation Motion diagram, motion graphs, interaction diagram, force diagram, events 1. Explain. How did you choose your key events? 2. Describe. While it is slowing down, what is the elevator interacting with? C: Word Representation Describe motion (no numbers), explain why, assumptions Did you explain why it slows down? What are we assuming about the acceleration? 23

24 D: Mathematical Representation Describe steps, complete equations, algebraically isolate, substitutions with units, final statement Did you use your sign convention to write the F net without using vector arrows? Did you use our guidelines for significant digits? E: Evaluation Answer has reasonable size, direction and units? Explain why. B: Sample Problems Use your solution sheets to answer the following questions. Is the size of the tension force reasonable? How can you tell compared with gravity? 1. Sunjamming. A "sun yacht" is a spacecraft with a large sail that is pushed by sunlight. Although such a push is tiny in everyday circumstances, it can be large enough to send the spacecraft outward from the Sun on a cost-free but slow trip. Your spacecraft has a mass of 900 kg and receives a steady push of 20 N from the sun. You many assume that is the only force acting on it. It starts its trip from rest. How far will it travel in 1.0 days and how fast will it then be moving? 2. Stopping a Neutron. When a nucleus captures a stray neutron, it brings the neutron to a stop in a distance of 1.0 x m (equal to the diameter of the nucleus) by means of the strong nuclear force. A stray neutron with an initial speed of 1.4 x 10 7 m/s is captured by a nucleus. You may assume that the strong force on the neutron is constant and is the only important force. Find the magnitude of strong force. The neutron's mass is 1.67 x kg. 3. Two People Pull. Two people are having a tug-of-war and pull on a 25 kg sled that starts at rest on frictionless ice. The forces suddenly change as one person tugs harder with a force of 92 N compared with the other person s force of 90 N. How quickly is the sled moving after 1.5 s? 4. Take Off. A Navy jet with a mass of 2.3 x 10 4 kg requires an airspeed of 85 m/s for liftoff. The engine develops a maximum force of 1.07 x 10 5 N, but that is insufficient for reaching takeoff speed in the 90 m runway available on an aircraft carrier. What minimum force (assumed constant) is needed from the catapult that is used to help launch the jet? Assume that the catapult and the jet's engine each exert a constant force over the 90 m distance used for takeoff. Answers: (1) 8.29 x 10 7 m, 1.92 x 10 3 m/s, (2) 16.4 N, (3) 0.12 m/s, (4) 8.16x10 5 N 24 Adapted from Cummings, K., et al, Understanding Physics. Wiley, 2004

25 Velocity (m/s) SPH3U: Interaction Forces A: Truck vs. Car! 1. Predict. (Individually) Imagine a car and a truck push on one another or collide. We want to explore the forces that arise in a few of these situations. For each situation consider two possible forces: the force the truck exerts on the car, the truck, FC T FT C, and the force the car exerts on. Decide based on the situation, whether each force is present and, if both are, compare their magnitudes. When finished, we will record your results on the board. Situation Exists? Compare (<, >, =) a) A truck pushes a stalled car from behind. They move together at a constant velocity. b) A fast moving car hits a truck at rest. c) A fast truck hits a car at rest. Recorder: Manager: Speaker: FT C FC T d) A truck tows a car. They are speeding up together. 2. Explain. Why, according to common sense, someone might decide that, in example (c), the truck exerts the greater force. B: Analysis - Kinematics Consider the collision between a quickly moving truck and a car at rest, example (c) from part A. We will model this with a large and small dynamics cart (500 g, 250 g). To the right is a graph showing the v-t data for each throughout the collision. The positive direction is to the right. 1. Explain. How can we tell that the dotted vertical lines correctly represent the starting and ending moments of the collision? Time (s) Large Cart Small Cart 2. Interpret. What is the duration of the collision? 3. Calculate. Use the velocity information to find the average acceleration (including direction) of each cart during the complete collision. Show all your work. 25

26 4. Explain. Which cart experienced the greater acceleration? Is this surprising? Describe, in an intuitive way, why this seems reasonable. 5. Reason. Imagine the carts were vehicles in a collision. Which one would you prefer to be in? Explain. C: Analysis - Forces It is clear from the data and your calculations that the small cart reacts more during the collision its acceleration is the greatest. But this is not the end of the story. Acceleration is the result of force, and we have not yet found the forces responsible. In this collision, the forces the carts exert upon one another are much larger than the force of friction. Therefore it is reasonable to ignore friction and assume that there is only one important horizontal force acting on each cart. 1. Represent. Draw an ID for the two carts with each as a separate system. Draw an for each cart. Label the forces FL S, meaning the force of the large cart on the small cart, and FS L, meaning the force of the small cart on the large cart. ID s 2. Calculate. Find the magnitude of the forces on your s using your acceleration results. Watch the signs! 3. Explain. How does the magnitude of FL S compare with FS L? Is this result surprising? Why? 4. Interpret. The force results seem like a contradiction of our common sense. We must re-interpret what our common sense is actually telling us. When we observe a collision between a car and truck, are we observing forces or accelerations? Explain. 5. Explain. Another strange aspect of this result is that forces of equal size produce such different acceleration results. How is this possible? 26

27 SPH3U: Newton s Third Law The case we have just studied of colliding carts points to a very general law about forces. The idea that the interaction forces between two objects (the carts) are equal in size holds true for all physical objects. This idea is known as Newton s 3 rd Law. Recorder: Manager: Speaker: When objects interact, a pair of forces is always produced they are two parts of one interaction. We call these two forces a third law force pair. The two forces that are members of the same third law pair share some important characteristics. the same magnitude opposite directions the same type (gravitational, normal, tension, etc.) start and stop acting at the same time act on different objects We can use the 3 rd law notation for forces to help show these relationships. Fn car truck means the normal force of the car acting on the truck. According to Newton s 3 rd law, the partner to this force in a 3 rd law pair is F. n truck car A: Exploding Carts! Your teacher has two identical dynamics carts on a track with a spring compressed between them. Your teacher will release the spring and we would like to consider the interval of time when the spring is expanding and affecting the carts. 1. Represent. Draw an ID for the two carts, with each as a separate system. Draw a for each cart. 2. Predict. Based on your diagrams, make a prediction comparing the velocity of each cart after the spring is released. Explain. ID s 3. Test. (as a class) Observe the results. Do they agree with your predictions? 4. Predict and Test. An extra mass is added to the cart with the spring. How do you think the s and resulting velocities change? Explain. You will test as a class. s B: The Apple and the Earth The story goes that our friend Sir Isaac Newton made a great discovery while he was sitting under an apple tree and an apple happened fall down on him. 1. Represent. Draw an ID and for the apple while it is at rest on the ground. Label each force using the 3 rd law notation. 2. Reason. Emmy says, The two forces on the must be third law pairs - they are equal in magnitude and opposite in direction. Do you agree or disagree? Explain. ID 27

28 3. Represent. Draw an ID and two s for the apple and the earth while the apple is falling. ID Apple Earth 4. Reason. Marie says, I think both the apple and the earth should be accelerating. Do you agree or disagree? Explain. 5. Reason. Isaac says, The earth clearly doesn t move, so I don t believe that it experiences an equal force to the apple. Do you agree or disagree? Explain. 6. Calculate. The apple has a mass of 0.2 kg. What is the magnitude of the force of gravity it experiences? Calculate the apple s acceleration using Newton s 2 nd law. 7. Calculate. The earth has a mass of 6.0 x kg. What is the magnitude of the force of gravity it experiences? Calculate the acceleration of the earth. 8. Explain. Based on your results from the previous questions, why is it understandable that most people think that the earth does not experience a force due to the apple, just like Isaac? C: Physics on Ice You have brought your little cousin out skating for the very first time. Both of you are standing on the ice wearing skates (no friction) and are facing one another. Your little cousin is a bit timid and needs to hold on to your scarf. 1. Represent and Calculate. She holds on while you gently pull the scarf with a 6 N force to start her moving. Her little mass is 17 kg. Draw a for her and determine her speed after pulling for 2.0 s. Little Cousin 2. Reason. Albert says, I understand why the cousin speeds up you are pulling on the scarf and she holds on. But I don t predict you will move. Your cousin is only holding on, not pulling. And, in any case, she is much smaller so she couldn t pull you anyways. Do you agree or disagree? Explain. You 3. Represent and Calculate. Draw a for yourself on the ice with your cousin. Use your actual mass to determine your speed after the same 2.0 seconds of pulling. 28