INTRODUCTION

A car is started from rest on a variety of shapes of tracks (hills, valleys, loops, straight track) and the speeds of the car at various points along the track are measured using a photogate connected to a Smart Timer. The potential energy is calculated from the measured height and the kinetic energy is calculated from the speed. The total energy is calculated for two points on the track and compared.

The height from which the car must be released from rest to just make it over the loop can be predicted from conservation of energy and the centripetal acceleration. Then the prediction can be tested on the real roller coaster. Also, if the car is released from the top of the hill so it easily makes it over the top of the loop, the speed of the car can be measured at the top of the loop and the centripetal acceleration as well as the apparent weight (normal force) on the car can be calculated.

THEORY

The total energy (E) of the car is equal to its kinetic energy (K) and its potential energy (U).

E = K U (1)

(2)

where m is the mass of the car and v is the speed of the car.

U=mgh (3)

where g is the acceleration due to gravity and h is the height of the car above the position where the potential energy is defined to be zero.

If friction can be ignored, the total energy of the car does not change. The Law of Conservation of Energy is slot maschinen stated as

E = constant

Figure 1: Step Configuration

1. Configure the track as shown in Figure 1. Attach a photogate to the straight portion at the bottom, positioned to measure the speed of the car just after it reaches the straight part (on the second peg from the left). Also put the catcher on the end of the straight part to keep the car from going off the end of the track.

2. Place the Mini Car at the top of the step on the left. Mark on the white board where you start the car. Measure the initial height of the car: Measure from the table to the center of mass of the car. Note that the center of mass of the car is approximately at the slot where the flag is inserted. The exact center of mass can be determined by balancing the car. Measure the car’s mass.

3. Place the car at the bottom on the flat part of the track and measure the height of the car from the table.

4. Place the car at the top and release it from rest. Use the photogate and Smart Timer (set on the Velocity: One Gate Mode) to measure the speed of the cart at the bottom of the step.

5. Calculate the initial total energy of the car.

6. Calculate the final total energy of the car.

7. How much energy is lost? Where does it go?

8. Calculate the percent of total energy lost.

9. Place the 50g mass on the car and repeat steps 2 through 8 above.