LAB #7: ROTATIONAL DYNAMICS AND THE CONSERVATION OF ENERGY

Transcription

1 OBJECTIVES: LAB #7: ROTATIONAL DYNAMICS AND THE CONSERVATION OF ENERGY To use the Law of Conservation of Energy to study the motion of a ball. EQUIPMENT: Equipment Needed Qty Equipment Needed Qty Rotational Dynamics Container 1 Balance 1 Measuring Equipment Tray 1 Three-Legged Ring Stand w/rod 1 Three-Finger Clamp 1 Double-V Clamp 1 Wooden Ball Track 1 Meter Stick 1 Carbon Paper White Paper SAFETY REMINDER Follow all safety instructions. Keep the area clear where you will be working and walking. THINK SAFETY ACT SAFELY BE SAFE! INTRODUCTION: In this lab you will be using the Law of Conservation of Energy to determine the velocity of a ball as it rolls off the end of a track. You will check your result by then predicting where it will land on the floor. PROCEDURES: Answer all of the questions on this handout. PART 1: Initial Measurements For later calculations you will need the mass of the ball, so measure it now. 1. What is the mass of the ball in grams?

2 2. What is the mass of the ball in kilograms? Set up your ramp as shown in Figure 1. Figure 1 shows how the clamps should be arranged. In Figure 2, have the end of the ramp extend slightly off of the lab bench. Attach the double-v clamp to the tripod stand. Insert the 3-finger clamp into the other notch of the double-v clamp, and hold one end of the wooden track with the 3- fingers. Allow the other end of the wooden track to extend off of the lab bench as shown in Figure 2. Make sure that the ball will roll off the end of the ramp without hitting the table. Figure 1 Use the inclinometer to measure the angle of the ramp, θ. 3. What is the angle of your ramp, θ? Find a convenient spot near the top of the ramp where you can release the ball from rest. It should be a place where you can hold the ball still while making measurements, and be able to replace it again, later. A possibility would be to push it up against the 3-fingered clamp. Measure the change in height, h, for the bottom of the ball from its position at the top of the ramp to the point where it leaves the bottom of the ramp. See Figure 2. Measure the height of the ball above the floor as it leaves the ramp. We will call this height H. Figure 2 h θ Bench

3 4. What is the ball s change in height, h, from the top to the bottom of the ramp? 5. What is the height of the ball, H, above the floor as it leaves the ramp? 6. What is the ball s initial potential energy when it is at the top of the ramp relative to its position when it leaves the ramp at the bottom? 7. What is the ball s initial kinetic energy when it is at the top of the ramp? 8. What is the ball s kinetic energy when it leaves the ramp at the bottom? PART 2: Determining the Ball s Velocity as It Leaves the Ramp As the ball rolls down the ramp we will assume that it is rolling without slipping. This means that it is translating and rotating, such that v = ω r. At the bottom, its kinetic energy is then part translational and part rotational. Its translational kinetic energy is given by KE T = 2 1 m v 2, and its rotational kinetic energy is given by KE R = 2 1 I ω 2. For a sphere that is rolling without slipping we have that I = 5 2 m r 2,

4 and ω = r v. So in terms of its mass and velocity the ball s rotational kinetic energy is given by KE R = 2 1 ( 5 2 m r 2 ) ( r v ) 2 = 5 1 m v 2. The ball s total kinetic energy is then KE = KE T + KE R = 2 1 m v m v 2 = 10 7 m v 2. Equating this with the answer to question 5 yields the ball s speed as it leaves the end of the ramp. 9. What is the ball s speed as it leaves the ramp? PART 3: Determining Where the Ball Will Land After the ball leaves the end of the ramp it is in free fall. We will use the velocity of the ball as it leaves the ramp to determine where it will hit the floor. Use the ball s speed as it leaves the ramp, and the inclination of the ramp, to determine the ball s initial horizontal and vertical velocities as it begins its free fall motion. 8. What is the ball s initial horizontal velocity? 9. What is the ball s initial vertical velocity? Given the ball s initial height, H, from floor as it leaves the ramp, and its initial vertical velocity, determine the ball s time of flight, that is, how long it will take to hit the floor. 10. What is the ball s time of flight?

5 Using the ball s initial horizontal velocity and its time of flight, you can determine how far, R, it will travel horizontally before hitting the floor. 11. How far horizontally, R, will the ball travel during its free fall motion? Using the plumb bob, determine the point on the floor directly below the end of the ramp. From this point, measure horizontally a distance R. This will be your impact point, that is, where you expect the ball to land. See Figure 3. Figure 3 Bench R The last page of this lab is your target sheet. Place the target sheet on the floor with the + at your target point. Place a sheet of carbon paper on top of your target sheet, and another piece of white paper on top of the carbon paper. Tape these sheets down with a piece of masking tape along one edge. When you are ready, call your instructor over to watch. Release the ball from rest at its initial point on the ramp and hopefully (theoretically) it will land right on the +. Hand in your target sheet with your lab. 12. How far from the + was your actual impact point? 13. What is the percent difference between your theoretical value for R and the experimental R? 14. If you missed the +, what factors do you think contributed to your error?