Suppose you have two equal mass objects both on a gentle incline. One is a glide

Question

Suppose you have two equal mass objects both on a gentle incline. One is a glider on an air track while the other is a ball on a straight slope. The air track and the slope have the same slope angle. You release them at the same time and at the same distance from the bottom of the slope. You note that neither loses any significant amount of energy to friction as the air track has very low friction and the ball rolls down without slipping or sliding.

a) Explain what type of energy both objects have just before they are released. Do both objects intially have the same amount of energy?

b) Explain what type of energy both objects have just before they reach the bottom of the slope. Do both objects have the same amount energy when they reach the bottom of the slope.

please explain each part in detail. Thanks!

Explanation / Answer

a) if they have the same mass and are the same vertical height above the ground and are both motionless, they have the same amount of potential energy, equal to mgh

b) at the bottom they have kinetic energy; the glider has only translational kinetic energy; the ball has both translational and rotational kinetic energy

if they lost no energy to friction, then they have the same total energy, but since some of the ball's energy went into rotation, it will have a slower linear speed down the incline, and will reach the bottom after the glider

their total energy is the same, but for the glider

1/2 mv^2 = mgh

while for the ball

1/2 mv^2 + 1/2 I w^2 = mgh

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