Toy Car Ramp Data With a Wall and Two Floors
Three groups test a toy car released from rest at heights of 10, 20, 30, and 40 cm on a ramp. Each height is tried three times, and the distance the car rolls along the floor is measured. Group A uses a smooth tile floor; groups B and C use carpet. Group A's mean distances are 44 cm, 90 cm, 133 cm, and 180 cm. One Group A trial from 30 cm reads 400 cm because the car hit a wall 4 m away and students recorded the wall distance. Group B's distances are about half of Group A's at every height. A student claims the data show that doubling the release height doubles the distance, so the car's energy must double. Another student says the 400 cm trial proves the car can gain energy from a collision. The teacher asks the class to decide which trials to keep and what the data actually support.
1. Should the 400 cm trial be included in the 30 cm mean? Justify using the experimental design and the meaning of the measurement.
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Exclude the 400 cm trial from the 30 cm mean. The measurement is censored by the wall: the car did not finish a free roll, so 400 cm records the distance to the wall, not the distance the car would have traveled. Including it would inflate the mean and break the comparison with the other heights. The correct handling is to report it separately as 'at least 400 cm' or discard it with a stated reason, then use the other two trials. This is a procedural outlier, not evidence of extra energy.
2. Using Group A's remaining data, evaluate the claim that doubling release height doubles distance. Support your answer with a ratio calculation.
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With the 400 cm trial removed, the remaining Group A means are about 44, 90, 133, and 180 cm. Doubling from 10 to 20 cm gives 90/44 ≈ 2.05; doubling from 20 to 40 cm gives 180/90 = 2.0. Quadrupling from 10 to 40 cm gives 180/44 ≈ 4.1, close to 4. The 30 cm value, 133 cm, is close to the 132 cm predicted by proportionality. So the data support the claim that distance is roughly proportional to release height over this range. That is consistent with gravitational potential energy being proportional to height and with a roughly constant friction force, but the experiment measures distance, not energy directly.
3. Group B's distances are about half of Group A's. Explain this using energy transfer, and state whether it contradicts conservation of energy.
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Carpet exerts a larger friction force than tile. The car leaves the ramp with about the same kinetic energy at a given height, but on carpet friction does more work per centimeter, so the car stops in a shorter distance. The missing mechanical energy becomes thermal energy in the car, carpet, and floor. Half the distance does not mean half the energy was lost or that energy disappeared; it means the same initial energy was dissipated over a shorter path. This is consistent with conservation of energy, not a contradiction.