Model a rolling system’s total kinetic energy by combining centre-of-mass translation with rotation, then apply energy conservation across its motion.
(7 points, suggested time 13 minutes)
A wooden wheel of mass M, consisting of a rim with spokes, rolls down a ramp that makes an angle θ with the horizontal, as shown above. The ramp exerts a force of static friction on the wheel so that the wheel rolls without slipping.
In a second experiment on the same ramp, a block of ice, also with mass M, is released from rest at the same instant the wheel is released from rest, and from the same height. The block slides down the ramp with negligible friction.
Which object, if either, reaches the bottom of the ramp with the greatest speed? Wheel Block Neither; both reach the bottom with the same speed.
Briefly explain your answer, reasoning in terms of forces.
Briefly explain your answer again, now reasoning in terms of energy.
1 point
Correct answer: Block
No credit for answer without explanation.
For a correct explanation in terms of forces 1 point
Example: The wheel experiences a counteracting frictional force, so the block has a greater net force exerted upon it and therefore has greater acceleration.
1 point
For a correct explanation in terms of energy conservation Example: Both object-Earth systems lose the same amount of potential energy and therefore gain the same amount of kinetic energy. With the ice block - but not the wheel - all the kinetic energy is translational, and none is rotational, so the block is faster.
Note: For parts (a) and (b), quantities that are proportional to mechanical energy, rather than energy itself, may be calculated, because terms like g or the ball's mass do not change during the experiment.