Unit 3: Newtonʼs Laws NAME: Text: Chapter 5: All sections of Chapter 5. Chapter 6: All sections of Chapter 6. Questions (p. 106-7) 1, 3, 7, 8, 10, 12 Problems (p. 108-15) #1: 3, 4, 5, 7, 10, 12 #2: 19, 31, 32, 35, 47, 48, 49, 50, 84 #3: 57, 59, 76, 82, 97, 101 Questions (p. 130) 3, 4, 5, 6, 10 Problems (p. 131-39) #4: 3, 7, 16, 17, 20, 30, 33, 34 (coefficient of friction) #5: 41, 45, 47, 55, 59, 60 (centripetal acceleration) #6: 87, 92, 97, 99, 107, 109 Vocabulary: Inertia, force, net force, tension, weight, normal force, friction, static friction, kinetic friction, terminal speed, drag coefficient, coefficient of friction, Newton (as in unit of force) Math: definitions:!! F = m a! f = µn derived formulas: w = mg w! = mgcos" w = mgsin! skills: no new math skills Key Objectives: state, explain and give examples of Newton s 3 Laws of Motion. compare and contrast mass and weight. define force, and explain its units (i.e. what is Newton?) draw and label and appropriate free-body diagram for any given situation/word problem. define friction and describe its effects on objects. define terminal speed, explain the factors that affect it, and describe what happens to the frictional forces, weight, and net force on an object that is freely falling. solve a variety of word problems involving multiple applied forces, tensions, and frictional forces. 2011-12
Free Body Diagrams I NAME: The first step in solving problems involving Newton s Laws is to draw a diagram of the situation. By making a drawing showing all the forces acting on a body, and knowing something about the bodies motion, you can then write equations based on Newton s Second Law:!F = ma, sometimes written as F net = ma. Part 1: Finding the Net Force. For each of the following situations, state the direction of the net force, if any. 1. A car driving to the right at constant speed. 2. A car driving to the right and speeding up. 3. A car driving to the left and slowing down. 4. A car driving up a straight steep hill at constant speed. 5. A car driving up a straight hill and slowing down. 6. A car driving in a circle at constant speed. 7. A helicopter hovering in the air. 8. A plane climbing at constant speed. 9. A plane climbing and speeding up. 10. An elevator going up at constant speed. Part II: Identifying the individual forces. For each of the situations below, draw all the individual force vectors, and then state what the net force is. Do not ignore air resistance or other forms of friction. If forces are of equal magnitude, draw them the same length. If not otherwise stated, assume motion is to the right. 1. A person standing still in the hallway. 2. A car traveling down the highway at constant speed. 3. A car traveling down the highway at increasing speed. 4. A person standing in an elevator that is not moving. 5. A person sitting in a wagon and being pulled to the left at an increasing velocity. side 1
Free Body Diagrams I NAME: 6. A person coasting and slowing down on a bicycle. 7. An airplane flying at constant velocity. 8. An airplane flying with increasing speed. 9. A person riding an elevator up at constant velocity. 10. A helicopter hovering in the air. 11. A person riding an elevator traveling up at an increasing speed. 12. A car traveling down the road with a constant acceleration. 13. A helicopter coming down at constant speed. 14. A person traveling up in an elevator, but with a decreasing velocity. side 2
Free Body Diagrams I NAME: 15. A box sitting at rest on hill. 16. A box with an initial velocity up a hill, but slowing down. Include friction. For each of the following diagrams, draw a free body diagram for each object. Correctly label each force in your diagram. (T = tension; W = weight; f = friction; N = normal force) All the pulleys are massless and frictionless, all the surfaces are frictionless. 17. Two masses connected by a string around a pulley. m1 m2 18. Little mass connected with a string to big mass on a horizontal table. m1 m2 19. Little mass sitting on a big mass, which is on a table and being pushed to the right. F m1 m2 20. Little mass in front of a big mass which is being pushed to the right. F m1 m2 21. Do questions 18 to 20 again, but this time include a frictional force between any appropriate surfaces (but the pulleys are still frictionless and don t worry about air.) side 3
ABRHS PHYSICS Force Problems I NAME: 1. A car of mass 1000 kg is accelerating with a constant rate of 1.5 m/s 2. What is the net force acting on the car? 2. An airplane is accelerating down the runway. The mass of the airplane is 15,000 kg. If the engines are producing a net thrust of 45,000 N, what is the acceleration of the airplane? 3. There is a net force of 200 N acting on a girl on a skateboard. If her acceleration is 4 m/s 2, what is her mass? 4. Tony is pulling Fred, who is sitting in a wagon. Tony is pulling with a force of 250 N. Fred and the wagon have a combined mass of 75 kg. If there is also a frictional force of magnitude 100 N acting on Fred, what is Fred's acceleration? 5. Sasha is pushing Kara with a force 350 N. Kara has a mass of 50 kg. If Kara is accelerating with a rate of 2 m/s 2, what is the magnitude of the force of friction acting on Kara? 6. A car of mass 1500 kg is accelerating with a rate of 3 m/s 2. If the magnitude of the force of friction is 6000 N, how much force must the engine be producing? 7. You are in your car, mass 1500 kg, traveling down the highway with a speed of 25 m/s. You see traffic ahead and apply the brakes. You slow down to 15 m/s in 4 seconds. What was the net force on the car? 8. A happy physics student wants to determine how much force she can produce. Starting from rest, she accelerates and covers 5 meters in only 1.5 seconds. If she has a mass of 55 kg, what was the net force on her? 9. A skateboarder, mass 75 kg, coasts from 15 m/s to 10 m/s over a distance of 25 meters. What was the magnitude of the force of friction acting on the skateboarder? 1. 1500 N 2. 3 m/s 2 3. 50 kg 4. 2 m/s 2 5. 250 N 6. 10,500 N 7. 3750 N 8. 244 N 9. 188 N
ABRHS PHYSICS Force Problems II NAME: 1. A space ship in interstellar space has a mass of 1,250,000 kg. If it accelerates at a constant rate of 3.5 m/s 2 for 1 hour, a. How much faster is it traveling after that hour? b. How much does the spaceship weigh in interstellar space? c. How much force is needed to keep the spaceship traveling with a constant velocity? Explain. 2. You are really bored one day and decide to see what happens if you really accelerate on a skateboard. You tie a rope to a car and get on your skateboard, and have a friend drive the car. The force of the car pulling you is a constant 250 N, and the magnitude of the force of friction is a constant 35 N. Assuming your mass (with the skateboard) is 80 kg and that you start from rest, a. What is your acceleration? b. How fast would you be going after a total of 2 seconds? c. How fast would you be going after a total of 15 seconds? d. What would happen if your friend had to hit the brakes in the car suddenly? e. Why should you never, ever do this? 3. Imagine you (mass 65 kg) are in an elevator at the bottom of the Prudential building. You then accelerate up at a constant rate of 2 m/s 2 for 1.5 seconds. a. What is the net force acting on you? b. What is your weight? c. What must be the support force acting on you? d. How fast are going at the end of this? side1
ABRHS PHYSICS Force Problems II NAME: 4. Still in the elevator, you are traveling up with a constant velocity (your answer to letter d above.) for a time of 30 seconds. a. What is the net force acting on you? b. What is your weight? c. What must be the support force acting on you? d. How fast are going at the end of this? 5. Still in the elevator, you are traveling up with the velocity from above when the elevator slows down at a rate of 2 m/s 2 for a time of 1.5 seconds. Then the doors open and you get off the elevator. a. What is the net force acting on you while slowing down? b. What is your weight? c. What must be the support force acting on you while slowing down? d. How fast are going at the end of this? 6. A 15000 N car is driving down the road with an initial velocity of 12 m/s. The car then speeds up to a final velocity 20 m/s in a time of 11 seconds. If the magnitude of the force of friction acting on the car during this speeding up was 2500 N, how much force did the engine have to produce for this acceleration? 7. You do a lab in which a friend pulls you on a skateboard with a constant force. You start from rest, and are pulled for a distance of 7 meters, at which point your friend stops pulling and you coast to a stop in 14 meters. (That means the total distance you were pulled and coasted was 21 meters.) The time it took your friend to pull you the 7 meters was 6.5 seconds. You and the skateboard have a mass of 60 kg. With how much force did your friend pull you? 1. a) 12,600 m/s b) 0 N c) 0 N 2. a) 2.7 m/s 2 b) 5.4 m/s c) 40.5 m/s d) you continue at 40.5 m/s and smash into car e) you will die 3. a) 130 N up b) 650 N down c) 780 N d) 3 m/s up 4. a) 0 N b) 650 N c) 650 N d) 3 m/s 5. a) 130 N down b) 650 N c) 520 N up d) 0 m/s 6. 3590 N 7. 30 N side2
Force Problems III NAME: 1. A 760,000 N plane is at rest on the runway. It then constantly accelerates down the runway, covering 650 meters in a time of 20 seconds. The magnitude of the force of friction acting on the plane while it was accelerating down the runway was 250,000 N. What was the force of the engines on the plane (thrust)? 2. You are having an enjoyable day in Boston going up and down the elevators in the Prudential Building. You are at the top of the building and press the down button. You also happen to be standing on a great metric bathroom scale, and you notice that your weight reads only 600 N while you are accelerating down. (Your real mass is 65 kg.) What was your acceleration? 3. A 150 gram mass is suspended by a string and is attached to a cart on a level track that has a mass of 750 grams. (Like the lab setups.) If the system is frictionless, what is the tension in the string? 750 gram cart lab table 150 gram hanger 4. Two masses are connected by a string around a massless, frictionless pulley. Mass m is 3 kg. The system is accelerating at a rate of 2.5 m/s 2 in a clockwise direction. What is the mass of n and what is the tension in the string? m n 1. 497,000 N 2. 0.77 m/s 2 down 3. 1.25 N 4. 37.5 N & 5 kg
Force Problems IV Include a correctly labeled free body diagram in each problem. NAME: 1. The Turkish Twist is a classic amusement park ride in which the riders stand in a tube. The tube spins around, and then the floor drops down, leaving the riders stuck to the wall. If the radius of the tube is 3 meters, and the coefficient of friction between the rider and the wall is 0.4, what is the minimum rotation speed (in rpm) of the ride? 2. A force F is pushing a big box M, which in turn is pushing a little box m, as shown in the diagram. The coefficients of friction are as shown. What is the minimum force F so that m stays suspended? µ 2 F m 1 m 2 µ 1 3. A car is driving around a curved, banked road, base angle! and radius r. If the coefficient of friction between the tires and the road is µ, what is the fastest the car can travel around the curve without sliding. Answers: 1. 27.6 rpm 2. F = (µ 1 + 1/µ 2 )(m 1 + m 2 )g 3. v 2 = rg[(sin! +µcos!)/(cos! µsin!)]
Newtonʼs Laws Circular Motion NAME: For each of the problems, include a correctly labeled free-body diagram. Identifying all the forces involved in these problems is the key to doing them correctly. Remember that centripetal force is just a fast way of saying that the net force is causing a centripetal acceleration. 1. A 1750 kg car is traveling around in circles in a flat level parking lot. It is going a constant 7.5 m/s with a constant radius of 22 m. a. What is the magnitude of the net force on the car? b. Where does the centripetal force come from? 2. A 65 kg person is riding the Turkish Twist at Canobie Lake Park. It has a radius of 5 meters and is spinning at a constant 20 rpm when the floor drops, leaving the person stuck to the wall. a. What is the magnitude of the net force on the person? b. Where does the centripetal force come from? 3. A conical pendulum has a length of 1.7 m and a mass of 250 grams. It is spinning such that the tension in the string is 4 N. a. What is the net force on the mass? m L b. How fast (m/s) is the mass spinning? 4. A conical pendulum has a length of 1.3 m and a mass of 0.6 kg. It is spinning around in a circle such that the angle! (in the diagram above) is 30º. How fast is the mass spinning? side 1
Newtonʼs Laws Circular Motion NAME: 5. A 75 kg person is riding a Ferris Wheel with a 25 meter radius. It is rotating at constant rate of 2 rpm. a. What is the magnitude of the net force on the person? b. What is the normal force on the person when at the highest point? c. What is the normal force on the person when at the lowest point? 6. A stunt rider on a motorcycle (total mass = 325 kg) is going around a loop-the-loop of radius 15 m. Imagine that they are going around the circle at constant speed of 17 m/s (probably not realistic, but hey it s a physics problem.) a. What is the normal force of the track on the motorcycle at the very top of the loop? b. What is the normal force of the track on the motorcycle at the very bottom of the loop? c. What is the minimum speed which the motorcycle can go around the loop and stay on the loop? 7. A car is going around a race track with a banked curve. If the car is going 45 m/s, and the radius of the curve is 250 m, what must be the angle of the bank so that friction is not needed to make the curve? Answers: 1 a) 4470 N b) friction between tires and road 2 a) 1430 N b) normal force of wall pushing rider to center. 3 a) 3.1 N b) 4.1 m/s 4) 1.9 m/s 5 a) 82 N b) 668 N c) 832 N 6 a) 3012 N, down! b) 9512 N c) 12.2 m/s 7) 39º side 2
NAME: Newtonʼs Laws Coefficient of Friction For each problem, include a correctly labeled free-body diagram. 1. A 40 kg box is being pushed by a constant force F across the floor. The coefficient of friction between the floor and the box is µ = 0.3. Find the acceleration for each of the following cases: a. F = 200 N, horizontally. b. F = 300 N at an angle of 35º above the horizontal. c. F = 300 N at an angle of 20º below the horizontal. d. F = 100 N, horizontally. (Be careful!) 2. A 15 kg box is being pulled by a force F at an angle of 30º above the horizontal. If the coefficient of friction between the box and the floor is µ = 0.4, what is the maximum F can be and not accelerate the box? 3. A mass M is resting on horizontal table and is attached by a string to a mass m that is hanging from a pulley. If the coefficient of friction between M and the table is µ, what is the maximum that m can be and not accelerate M? 4. A 250 gram mass is sliding with constant speed down an inclined plane with a base angle of 20º. What is the coefficient of friction between the mass and the inclined plane? side 1
NAME: Newtonʼs Laws Coefficient of Friction 5. A 0.5 kg mass is on an inclined plane with base angle of 30º. The coefficient of friction between the mass and the plane is 0.35. The 0.5 kg mass is attached by a string to a little mass m that is hanging from a pulley from the top of the ramp. If the system is to remain at rest, what are the minimum and maximum that m can be? 6. A 3 kg box is resting on top of a 5 kg box, which is on a horizontal table. The coefficient of friction between the box and the table is 0.3. If the bottom box is pushed by a horizontal force of 40 N, what is the acceleration of the boxes, assuming the little box stays on top of the big box. 7. In the previous problem, what must be the minimum coefficient of friction between the two boxes so that the little box stays on top of the big box? 8. A box slides from rest down an inclined plane with base angle 40º and then onto a flat horizontal table. The coefficient of friction between the box and both surfaces is 0.2. If the ramp is 1.5 meters long, how far on the table does the box slide before coming to rest? Answers: 1 a) 2 m/s 2 b) 4.4 m/s 2 c) 3.3 m/s 2 d) 0 m/s 2 2) 56.3 N 3) µm 4) 0.36 5) 0.098 & 0.4 kg 6) 2 m/s 2 7) 0.2 8) 3.65 m side 2
Lab 5-1: Newton's Second Law NAME: Purpose: 1. To determine an equation that describes the relationship between acceleration and applied force for an object of constant mass. 2. To determine an equation that describes relationship between acceleration and mass for an object undergoing a constant applied force. 3. To determine the general relationship between force, mass, and acceleration. Materials: 3 (three) 100 gram slotted masses 1 (one) 50 gram slotted mass 1 hanger 1 cart 2 extra 500 gram masses (bars) 1 string (~75 cm) 1 pulley system Procedure: 1. Set up the track, cart, pulley, hanger and motion detector as shown in the diagram below. 2 bars & all slotted masses lab table empty hanger 2. Record the mass of the cart, string and hanger on the other side of this sheet. 3. Make sure the track is level. The cart should not be rolling in either direction. Also, make sure that the string is attached to the pulley horizontally. 4. Put the cart on the track. Place the two extra 500 gram masses on the cart. Place all the slotted masses on the cart. Secure the slotted masses with some masking tape. (Just enough so that the masses stay in place.) Part I: Determining the effect of force on acceleration (with constant mass) 6. Pull the cart back to the middle of the track and hold it. Make sure that there is about 20 cm between the cart and the motion detector. Also, make sure that the hanger just reaches the ground as the cart reaches the end of the track; shorten the string if necessary. (Once the hanger hits the ground, there will no longer be an accelerating force.) 7. Start timing. When you hear the motion detector, release the cart. Don t let the cart slam into the end of the track! 8. To determine the acceleration of the cart, measure the slope of the best fit line of the velocity graph. Do this 3 times. 9. Repeat steps 6 to 8 above for seven more trials. For each new trial, transfer 50 grams from the cart to the hanger. If there are only 100 gram masses on the cart, switch a 100 gram from the cart with the 50 gram on the hanger After computing the best fits, simply record the results in the data table for Part I. Do not add any new masses to the system! The total mass that is being moved must remain constant for every trial. Part II: Determining the effect of mass on acceleration (with constant force) 10. Put the empty cart on the track, and remove any extra masses from the hanger. 11. Start timing. When you hear the motion detector, release the cart. 12. To determine the acceleration of the cart, measure the slope of the best fit line of the velocity graph 13. Repeat steps 10 to 12 above for six more trials. For each new trial, add 250 grams (0.25 kg) to the cart. Do not add masses to the hanger! (The applied force must remain constant.) If needed, use masking tape to secure loose masses. After determining the slopes of the best fit lines, simply record the results in the data table for Part II. Part III: Analyzing results. 14. Make the following graphs: Acceleration vs. Force from part 1 and Acceleration vs. Mass from part 2. If they are not linear, linearize them. Make sure that the graphs have the regression lines, equations and everything is labeled. Print out your results. side 1
Data for Part I: Lab 5-1: Newton's Second Law NAME: Mass of cart, hanger, string, extra masses and all slotted masses: kg NOTE: To calculate Applied Force, use the ratio of 9.8 N for each kilogram (Also remember that 1 kg is 1000 grams.) Mass Suspended (grams) 50 (just hanger) 100 (hanger + 50) 150 200 250 300 350 400 Applied Force (N).49 Acceleration (m/s 2 ) Data for Part II: Applied force exerted by the 50 gram hanger: 0.49 N Mass accelerated (kg) cart + hanger Acceleration (m/s 2 ) cart + hanger +.25 cart + hanger + 0.5 side 2
Lab 5-1: Newton's Second Law NAME: Questions: Part I: 1. What is the equation that describes the relationship between acceleration and applied force for your data? (Remember: slopes have units.) 2. Qualitatively, describe the relationship between acceleration and force for a given mass. Part II: 3. What is the equation that describes the relationship between acceleration and mass for your data? (Remember: slopes have units.). 4. Qualitatively, describe the relationship between mass and acceleration for a given force. Conclusion: 1. What is the relationship between force, mass, and acceleration for any body? (Combine your results from the two parts of this lab.) 2. In Part I, why did you have to move masses from the cart to the hanger to increase the force? Why could you not just take some extra masses that were lying on the table and put them on the hanger? 3. What is a Newton? 4. What does the slope of the Acceleration vs. Force graph physically represent? (Simplify the units first.) 5. What does the slope of the Acceleration vs. Inverse Mass graph physically represent?? (Simplify the units first.) side 3
Lab 5-2: Finding Friction NAME: Purpose: Devise a method to calculate the force of friction for the following two situations: a. A wooden block that is pulled across the lab table by a string attached to a hanging mass over a pulley. b. A wooden block that is sliding down an inclined ramp. Procedure: You can do these 2 tasks in either order. Task 1: Attach a string to a wooden block and attach a pulley to the end of the table. Put a hanger on the end of the string so that it accelerates the wooden block across the table. Devise a method to calculate the force of friction that is acting on the block. Describe your procedure, make a data table and show all your calculations here: side 1
Lab 5-2: Finding Friction NAME: Task 2: Attach a ramp to a pole to make an inclined plane. Without any strings, let the wooden block slide down the incline. Devise a method to calculate the force of friction that is acting on the block. Describe your procedure, make a data table and show all your calculations here: side 2
Lab 6-1: The Coefficient of Friction NAME: Purpose: To determine: a. the relationship between the normal force between two objects and the force of friction that acts between them. b. if the force of friction on a block sliding on the table or a track depends on the area of contact between the block and table. Materials: several slotted masses 1 wooden block 1 hanger 1 string (~75 cm) 1 pulley system Procedure: 1. Record the mass of the wooden block. Then, set up the track, block, pulley, hanger and motion detector as shown in the diagram below. wooden block, felt side down lab table hanger plus 100 gram mass 2. Make sure the track is level. A cart should not be rolling in either direction. Also, make sure that the string is attached to the pulley horizontally. (This can also be done on the lab table instead of the track.) 3. Open up LoggerPro. Add a 100 gram mass to the hanger, for a total pulling mass of 150 grams. For this first trial, do not have any extra mass on the wooden block. 4. Hold the block in the middle of the track, click on Collect, and then release the block. 5. To determine the acceleration of the block, measure the slope of the best fit line of the velocity graph. 6. Repeat the above to find the acceleration of the block for a total of eight different masses. For each new trial, add 50 grams to the wooden block. 7. Flip the wooden block on its side and repeat, recording your results in the second data table. Data: Mass of wooden block: kg Applied Force: 1.47 N Important: The total mass accelerated is always the total block mass, plus the 0.150 kg that are hanging over the edge of the lab table and any extra masses that you have put on the block! Tria l # extra mass on block (kg) total block mass (kg) total mass accelerated (kg) acceleration (m/s 2 ) Net Force (N) Friction Force (N) Normal Force (N) 1 0 2.050 3.100 4.150 5.200 6.250 7.300 8.350 side 1
Part 2: Block on its side. Tria l # extra mass on block (kg) 1 0 2.050 3.100 4.150 5.200 6.250 7.300 8.350 total block mass (kg) Lab 6-1: The Coefficient of Friction total mass accelerated (kg) acceleration (m/s 2 ) Net Force (N) Friction Force (N) NAME: Normal Force (N) Calculations: 1. For each trial, calculate the net force on the system from the total mass accelerated and the acceleration. Show your calculations for the first trial here, and record all your results in the data table above. 2. For each trial, calculate the force of friction on the system. Show your calculations for the first trial here, and record all your results in the data table above. 3. For each trial, calculate the normal force between the wooden block and the table. Show your calculations for the first trial here, and record all your results in the data table above. Graph: Using Graphical Analysis, make a graph of Frictional Force verses Normal Force for each trial. Don t forget labels, units, titles and regression lines. Also, make sure the origin is visible. Conclusion: 1. What are the equations that describes the relationship between friction and normal force for your data? (Include the y-intercept.) 2. Does the force of friction depend on the surface area of contact? 3. In general, what does the force of friction depend on? side 2
Lab 6-2: Centripetal Force NAME: Purpose: Whenever an object moves in a circle with constant speed and radius, the net force on the object is always directed to the center of the circle. The net force in this situation is given the special name, centripetal force, which simply means "center-seeking" force. Centripetal forces depend on an object's mass, speed, and radius of the circular path. In this lab, you will determine how centripetal forces depend on the speed of an object. Materials: 1 hanger 1 glass tube 1 rubber stopper 1 string (~1 m) small piece of tape 1 stop watch slotted masses (total of 200 grams) Procedure: 1. Find the mass of the rubber stopper, record it in the data table, and then set up your apparatus as shown in the diagram below. 0.75 m glass tube rubber stopper small piece of tape (keep this level while spinning the stopper) hanger with slotted masses 2. Adjust the length of the string so that there is 0.75m from the glass tube to the middle of the stopper. Attach a small piece of tape to the string a few centimeters below the bottom of the glass tube. (This will give you a reference point to keep the radius constant at 0.75 m while spinning the stopper.) 3. Without any additional masses on the hanger, practice spinning the stopper. You need to be able to spin the stopper in a horizontal circle over your head and keep the piece of tape at the same distance below the glass tube. Be careful not to hit any passersby while you are spinning the stopper! 4. Without any additional masses on the hanger, spin the stopper. When you are ready, time how long it takes for the stopper to make 30 revolutions. (This is easier if someone counts and someone else uses the stop watch.) Record your results. 5. Add 50 grams to the hanger, and repeat step #5. Do this four times, each time adding an additional 50 grams. Data: Mass of rubber stopper = kg Radius of circular path = 0.75 m side 1
Lab 6-2: Centripetal Force NAME: Note: While doing the lab, the only data you need to take is the third column of the data table (Time for 30 revolutions). The rest of the table is calculated. Mass hanging (kg) Weight hanging F c (N) Time for 30 revolutions (s) Period of 1 revolution (s) Circumference of circle (m) Speed of stopper (m/s).050.100.150.200.250 Graph: Complete the rest of the data table by doing the appropriate calculations. Make a graph of Centripetal Force vs. Speed. Make sure you can see the origin. This will NOT be a straight line. Linearize your data to find the relationship between force and speed. Make sure to include labels, units. titles and regression line. Include the linearized graph with this lab. Conclusion: 1. What is the equation that relates centripetal force and speed for your experimental setup? 2. Simplify the units of the slope of your equation. 3. What is the physical significance of the slope of this equation? 4. What is the general equation that relates Centripetal Force and Speed? 5. The rubber stopper did not actually travel in a horizontal circle. We should have measured the angle at which the stopper dipped below horizontal. Draw and label a correct force diagram for the rubber stopper. In addition, write out Newton s Second Law for the stopper for both components. 6. Since the analysis you did on your data ignored the dipping of the stopper, why did it work so well? (At least, it should have worked.) side 2
Lab 6-3: Terminal Speed NAME: Purpose: To determine the relationship between the force of air resistance (drag force) and speed for an object moving through the air. Discussion: To simplify problem-solving and focus on key ideas, we almost always ignore air resistance in this class. However, in this lab we will try to find the mathematical relationship between the force of air resistance (drag force) and the speed of an object through the air. We will drop coffee filters from a large height (stairwell). The large height is important because we are assuming that the coffee filters reach terminal speed pretty quickly so that the speed of the coffee filters as they fall is relatively constant. In this way, we can assume that the weight of the coffee filters is equal to the drag force. Materials: 35 coffee filters stopwatch tape measure Procedure: 1. Measure and record the drop height and the mass of 10 coffee filters. 2. Holding 1 coffee filter so that the flat part is on the bottom, release it from rest and record the time it takes the coffee filter to fall to the floor. 3. Repeat above, each time adding coffee filters so that they stack together, and always holding the flat part down. Fill in the chart below. (We are thus keeping the shape and surface area more or less constant, while changing the weight of the dropped object.) Data: Distance Fallen: m Mass of 10 Coffee Filters: kg Coffee Filters (#) Time to Fall (s) Weight of Coffee Filters (N) Average Speed (m/s) Coffee Filters (#) Time to Fall (s) Weight of Coffee Filters (N) Average Speed (m/s) 1 10 2 15 3 20 4 25 5 30 7 35 Calculations: 1. Calculate the average speed of each coffee filter as it fell and the weight of each set of coffee filters. Record your results in the data table above. 2. Graph Force vs Speed for your results. Linearize your results to find the equation that relates force and speed. side 1
Conclusions: 1. What is meant by the term terminal speed? Lab 6-3: Terminal Speed NAME: 2. How reasonable is it to say that the average speed of the coffee filters is equal to the terminal speed of the coffee filters? Explain. 3. Why would this lab NOT have worked if we just dropped the coffee filters off the lab benches? 4. Why can we say that the weight of the coffee filters is equal to the force of air resistance on the coffee filters? 5. What is the relationship between the speed of the coffee filters and the force of air resistance on them? 6. Imagine dropping a ball from a large height. Sketch 1) speed vs. time, 2) acceleration vs. time, and 3) height vs. time. (Keep everything positive and qualitatively make the sketches.) side 2