Unit 6. Forces and motion

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1 Unit 6. Forces and motion Index 1. What is a force? Forces and flexible objects. Hooke's law Forces and changes in velocity Simple machines Types of forces...12 Practice exam...14 Page 1 of 15

2 1. What is a force? A force is any influence that causes an object to change its velocity (which includes to begin moving from a state of rest) or a flexible object to deform. A force is a vector quantity. It is measured in the SI unit of newtons (N) and it is represented by the symbol F. 2. Forces and flexible objects. Hooke's law Hooke's law is a principle of physics that states that the force F needed to extend or compress a spring by some distance e is proportional to that distance. That is, F = k (l l 0 ) = k e where k is a constant factor characteristic of the spring l is the length measured each time l 0 is the initial length of the spring e is the extension Hookes's law is only a first order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. In fact, many materials will noticeably deviate from Hooke's law well before those elastic limits are reached. On the other hand, Hooke's law is an accurate approximation for most solid bodies, as long as the forces and deformations are small enough. The spring constant k is different for different objects and materials. It is found by carrying out an experiment. Exercises of Hooke's law 1. A spring extends 20 cm when we apply a force of 20 N on it. a) Calculate the value of the elastic constant of the spring. b) Calculate how much the spring extends when a force of 60 N is applied on it. Answers: a) 100 N/m b) 0.6 m 2. Calculate how much a spring with an elastic constant of 100 N/m extends when a force of 85 N is applied on it. Answer: 0.85 m 3. A spring extends 12 cm when a force of 18N is applied on it. Calculate: a) The value of the elastic constant of the spring. b) How much the spring extends when a force of 45 N is applied on it. Answer: a) 150 N/m b) 30 cm 4. A force of 2 N is applied on a spring with an elastic constant of 12 N/m and an initial length of 10 cm. Find out the final length of the spring. Answer: m Page 2 of 15

3 5. A spring whose elastic constant is 150 N/m is 35 cm long when no force is applied on it. Calculate: a) The force that should be applied on the spring so that its length becomes 45 cm. b)the length of the spring when a force of 63 N is applied on it. Answer: a) 15 N b) 77 cm 3. Forces and changes in velocity A force is any influence that causes an object to change its velocity. So, What is velocity and what are the types? Speed: Speed can be defined as how fast something moves or it can be explained more scientifically as the distance covered in a unit of time. Speed is a scalar quantity. There are two types of speed: - Average speed. The average speed of an object is defined as the distance traveled divided by the time elapsed. Unit in the SI m/s. - Instantaneous speed Let us Consider a cyclist riding, his velocities varies continuously depending on time, distance etc. At any particular instant if we want to find his speed its nothing but instantaneous speed You might think of the instantaneous speed as the speed that the speedometer reads at any given instant in time and the average speed as the average of all the speedometer readings during the course of the trip. Activities 6. While on vacation, Lisa traveled a total distance of 440 Km. Her trip took 5 hours. What was her average speed? Sol: 88 Km/h = 24.4 m/s She may not have been traveling at a constant speed of 88 Km/h. She undoubtedly, was stopped at some instant in time (perhaps for a bathroom break or for lunch) and she probably was going 100 Km/h at other instants in time. 7. In the 2008 Olympics, Jamaican sprinter Usain Bolt shocked the world as he ran the 100-meter dash in 9.69 seconds. Determine Usain's average speed for the race. Sol: 10.3 m/s 8. Ken is the star of the cross-country team. During a recent morning run, Ken averaged a speed of 5.8 m/s for 12.9 minutes. Ken then averaged a speed of 6.10 m/s for 7.1 minutes. Determine the total distance which Ken ran during his 20 minute jog. Sol: 7088 m Page 3 of 15

4 Velocity: It can be defined as speed having direction or displacement in a unit of time. Velocity is a vector quantity and it has both magnitude and direction. The difference is in speed is distance divided time but velocity is displacement divides by time. Distance: Distance is a scalar quantity representing the interval between two points. It is just the magnitude of the interval. Displacement: Displacement can be defined as distance between the initial and final point of an object. It is a vector quantity having both magnitude and direction. Now let's consider the motion of a physics teacher. The physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the average speed and the average velocity. The physics teacher walked a distance of 12 meters in 24 seconds; thus, her average speed was 0.50 m/s. However, since her displacement is 0 meters, her average velocity is 0 m/s. Remember that the displacement refers to the change in position and the velocity is based upon this position change. In this case of the teacher's motion, there is a position change of 0 meters and thus an average velocity of 0 m/s. 9. The Sun is km from Earth. Calculate the minutes light takes to reach the Earth. The speed of the light is m/s. Sol: 8.33 min. 10.An object is moving with a velocity of 23 m/s in the positive direction of axis x. The final position of the object is 8 m. Which was the initial position if the traveled time is 5 s? Sol: -107 m 11An object is moving with constant velocity along axis x. The initial position is 13 m and the final position of the object is 5 m. Which is its velocity if the traveled time is 4 s? Sol: -2m/s 12. A man was driving his car from his office to his home at 50 km/h. Thirty minutes later he realized that he forgot some important documents at the office. What constant speed he should drive the car so that he can return to the office within 12 minutes? Sol: 125 km/h Page 4 of 15

5 The average velocity is displacement / time. Displacement is final position - initial position, so 0-0 = 0 and 0/10 is 0 m/s The instantaneous velocity is for example time(s) displacement(m) Time of the segment(s) Instantaneous velocities(m/s) 2 8-0= 8 (4-0) = 4 8/4 = = 0 (7-4) = 3 0/3 = = -8 (10-7) =3-8/3 = -2.7 What is the instantaneous velocity at 1 s? We are talking about the first segment so the answer is 2 m/s What is the instantaneous velocity at 8 s? We are talking about the third segment so the answer is -2.7 m/s The negative sign means that the object is coming back. Activities. 13. Complete the table: time(s) displacement(m) Time of the segment(s) Instantaneous velocities(m/s) Page 5 of 15

6 What is the value of the average velocity? 14. What is the instantaneous velocity at a) 10 s b) 30 s c) 60 s 15. Complete the table: time(s) displacement(m) Time of the segment(s) What is the value of the average velocity? sol: a) 20 m/s b) 40 m/s c) 80 m/s Instantaneous velocities(m/s) Page 6 of 15

7 Sol: a) 1.5 m/s b) 0 m/s c) 3.5 m/s d) 1m/s 16. The position-time graph below represents the motion of South's basketball coach during the last sixteen seconds of overtime during this past weekend's game. Use the graph to answer the next several questions. a. Determine the total distance walked by the coach during these 16 seconds. b. Determine the resulting displacement of the coach during these 16 seconds. c. Determine the displacement of the coach after 12.0 seconds. d. At what time did the coach have the greatest displacement from his starting position? e. What was the fastest speed which the coach walked during any of the time intervals for the last 16.0 seconds? f. What was the average speed of the coach for these 16.0 seconds? Answer a. 24 m b. 0 m c. 6 md. 4-6 seconds and again at 14 seconds e. 4 m/s f. 1.5 m/s 17. Mr. H is preparing to show the class a Strobe demonstration when he realizes that his absentmindedness has struck once more. He left the strobe on the counter in the back of the lab after the last class period. Starting 1.0 meter from the front of the room, Mr. H walks quickly to the back of the lab, picks up the strobe and returns to the middle of the classroom. The position-time graph below represents his motion. Use the graph to answer the next several questions. Page 7 of 15

8 a. What is the total distance walked by Mr. H during these 8.0 seconds? b. What is the average speed of Mr. H during these 8.0 seconds? c. What is the average velocity of Mr. H during these 8.0 seconds? d. How fast did Mr. H walk during the first 5.0 seconds? e. How fast did Mr. H walk during the last 3.0 seconds? Answer a. 16 m b. 2.0 m/s c. 0.5 m/s d. 2.0 m/s e. 2.0 m/s Acceleration: We can easily define acceleration as change in velocity. This change can be in the magnitude (speed) of the velocity or in the direction of the velocity. Changes in the speed a = v- v 0 /t Example. A car is initially travelling at 4 m/s then accelerates at 5 m/s 2 for 7 s. How fast is it going after this time? Given: v 0 = 4 m/s a =a = v- v 0 /t so v = v 0 + a t a = 5 m/s 2 v = 4 + (5) (7) t = 7 s v = v =? v = 39 m/s 18. What is the acceleration in each segment? v(m/s) t(s) Sol.:a = 4 m/s 2, -2 m/s 2, 0m/s 2 Page 8 of 15

9 19. The velocity-time graph below represents the motion of a car on a city street. Use the graph to determine the acceleration values of the car at... a. 1.4 seconds. b. 6.8 seconds. c seconds. d seconds. Sol: a. 2.0 m/s/s b. 0.0 m/s/s c. 6.0 m/s/s d m/s/s 20. Jeremy has recently taken up snowboarding as a hobby. He is practicing making smooth turns while traveling up sloped inclines. The velocity-time graph below depicts his motion traveling up an embankment and part-way down. Use the graph to answer the following questions. a. Determine Jeremy's acceleration at 8.0 seconds. b. At what time did Jeremy begin to travel back down the embankment? Sol:a m/s/s b s Page 9 of 15

10 21. Look at the following graphs. They represent the motion of different objects. Which ones have acceleration? x v v a v a t b t c t d t e t x x v a x f t g t h t I t j t 4. Simple machines What is a Simple Machine?: Work is performed by applying a force over a distance. These simple machines create a greater output force than the input force; the ratio of these forces is the mechanical advantage of the machine. Simple machines have been used for thousands of years. These machines can be used together to create even greater mechanical advantage, as in the case of a bicycle. Lever: A lever is a simple machine that consists of a rigid object (often a bar of some kind) and a fulcrum (or pivot). Applying a force to one end of the rigid object causes it to pivot about the fulcrum, causing a magnification of the force at another point along the rigid object. There are three classes of levers, depending on where the input force, output force, and fulcrum are in relation to each other. Baseball bats, seesaws (balancín), wheelbarrows (carretilla) are types of levers. Inclined Plane: An inclined plane is a plane surface set at an angle to another surface. This results in doing the same amount of work by applying the force over a longer distance. The most basic inclined plane is a ramp; it requires less force to move up a ramp to a higher elevation than to climb to that height vertically. The wedge is often considered a specific type of inclined plane. Pulley: A pulley is a wheel with a groove along its edge, where a rope or cable can be placed. It uses the principle of applying force over a longer distance, and also the tension in the rope or cable, to reduce the magnitude of the necessary force. Complex systems of pulleys can be used to greatly reduce the force that must be applied initially to move an object. Page 10 of 15

11 Work input = F e d input = F r d output = Work output Activities 22. The arms of a horizontal lever are 0.2 m and 1 m long at opposite sides of the fulcrum. The shorter arm is loaded with the downward force of 500 Newtons at the end. What force should be applied at the lever longer arm end to balance the load? Sol: 100 N 23. John wants to move rock with a 120 cm crowbar. He puts the fulcrum 20 cm from the rock. If the weight of the rock is a 1960 N, How much force must he use to move the rock? Sol: 392 N 24. John weighs 40 kg and sits 1.2 m from the fulcrum of a seesaw. If Sally weighs 50 kg and sits on the other side, how far from the fulcrum must she sit to have the seesaw balance? Sol: 0.96 m 25. A man can push down with a force of 392 N. He has a 1.5 m long crowbar. The man is going to use the crowbar as a lever to lift the stone. The fulcrum is in 0.3 m from the stone. How heavy a stone could be the man could lift it using crowbar as a lever? Sol: 1568 N (160 Kg) 26. Alice and Barbara are playing on seesaw. Alice s weight is 35 kg, and she is sitting at the distance of 1.5 m from the fulcrum. Barbara is sitting at the distance of 1.3 from the fulcrum, and the seesaw is in balance. Could you determine Barbara s weight using this data? Sol: 40.4 Kg Page 11 of 15

12 5. Types of forces - Frictional force The friction force is the force exerted by a surface as an object moves across it or makes an effort to move across it. There are at least two types of friction force - sliding and static friction. Though it is not always the case, the friction force often opposes the motion of an object. For example, if a book slides across the surface of a desk, then the desk exerts a friction force in the opposite direction of its motion. Friction results from the two surfaces being pressed together closely, causing intermolecular attractive forces between molecules of different surfaces. As such, friction depends upon the nature of the two surfaces and upon the degree to which they are pressed together. - Weight The force of gravity is the force with which the earth, moon, or other massively large object attracts another object towards itself. By definition, this is the weight of the object. All objects upon earth experience a force of gravity that is directed "downward" towards the center of the earth. The force of gravity on earth is always equal to the weight of the object as found by the equation: - Gravitational force law W = m g where g = 9.8 N/kg (on Earth) and m = mass (in kg) (Caution: do not confuse weight with mass.) This law states that every massive particle in the universe attracts every other massive particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Gravitational force surrounds us. It is what decides how much we weigh and how far a basketball will travel when thrown before it returns to the surface. The gravitational force on Earth is equal to the force the Earth exerts on you. At rest, on or near the surface of the Earth, the gravitational force equals your weight. On a different astronomical body like Venus or the Moon, the acceleration of gravity is different than on Earth, so if you were to stand on a scale, it would show you that you weigh a different amount than on Earth. Each system in the galaxy, and presumably, the universe, suffer gravitational force. The push and pull of the gravitational force of the objects is what keeps everything in space from crashing into one another. Newton's law of universal gravitation extends gravity beyond earth. Newton's law of universal gravitation is about the universality of gravity. ALL objects attract each other with a force of gravitational attraction. Gravity is universal. Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force. So as the mass of either object increases, the force of gravitational attraction between them also increases. Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. So as Page 12 of 15

13 two objects are separated from each other, the force of gravitational attraction between them also decreases. The constant of proportionality (G) in the above equation is known as the universal gravitation constant. The precise value of G was determined experimentally by Henry Cavendish in the century after Newton's death. The value of G is found to be G = x N m 2 /kg 2 The units on G may seem rather odd; nonetheless they are sensible. When the units on G are substituted into the equation above and multiplied by m 1 m 2 units and divided by d 2 units, the result will be Newtons - the unit of force. Activities 27. Complete the table True False friction is a force that works in an opposite direction to movement of an object. There is always friction when an object is moving on Earth. Friction can only happen with large objects. Friction can happen with both liquids and solids. Friction can stop things from moving The Moon has no gravity Mass and weight have essentially the same meaning. To increase the weight of an object requires an increase in the mass of the object. Friction provides the force which "pushes" a car forward as it accelerates down the road. (Assume a flat road.) Bigger the distance between two masses lower the force between them 28. Choose the correct one 1). A boy sits halfway down a grassy slope. What force stops him sliding down? a. Weight b. gravity c. friction 2). On which surface will a toy sledge travel the furthest? a. carpet b. wood c. ice 3). Rougher surfaces have... a. greater friction b. less friction c. same level of friction 5. If you poured oil onto a wooden surface, the friction would... a. be reduced b. be increased c. remain the same. Page 13 of 15

14 Practice exam 1. If the speed of a sound is 340 m/s, how far from us would a person be if it takes us 5 s to hear her cries? Sol: 1700 m 2. An object is moving with a velocity 10 m/s in the negative direction of axis x. The object is initially at point A in x = 4 m. Find the position of the object at 5 s. sol: -46 m 3. A spring whose K= 50 N/m is 25 cm long when no force is applied on it. Calculate: a) The force that must be applied on the spring so that it becomes 45 cm long. b) The length of the spring when a force of 25 N is applied on it. Sol: a) 10 N b) 70 cm 4. What is the value of the average speed? And the value of the average velocity? And the instantaneous velocity at a) 3s b) 7 s c) 11 s? sol: a) 0,8 m/s b) 0 m/s c) 1m/s d) 0 m/s e) 2 m/s 5. What is the value of the acceleration at 5 s, 40 s, 80 s? Page 14 of 15

15 sol: 2 m/s 2, 0 m/s, 1m/s 2 6. John wants to move a 400 Kg. rock with a 1,5 m crowbar. He puts the fulcrum 30 cm from the rock. How much force must he use to move the rock? Sol: 980 N 7. Explain how an inclined plane and a pulley work. 8. Define and describe the factors that these forces depend on: a) frictional force b) gravitational force c) weight 9. Complete the table definition symbol unit example weight mass 10. The weight of a boy on the Earth is 441 N. What is the weight of this boy on Mars? What is the mass on the Moon, and the weight? Data: gravity on Mars = 3,7 m/s 2 and gravity on the Moon is 1,6 m/s 2 Sol: 166,5 N, 45 kg, 72 N Page 15 of 15

AP Physics I Summer Work

AP Physics I Summer Work 2018 (20 points) Please complete the following set of questions and word problems. Answers will be reviewed in depth during the first week of class followed by an assessment based