## Related questions with answers

An object is released from rest at the top of a ramp. If the ramp is frictionless, does the object’s speed at the bottom of the ramp depend on the shape of the ramp or just on its height? Explain. What if the ramp is not frictionless?

Solution

VerifiedCase 1. (no friction):

Applying equation 7.14, there is no other force doing work, so $W_{other}=0$.

Assume the potential energy is zero at the bottom of the ramp.

At the top of the ramp, speed was zero, so kinetic energy was zero.

$K_1+U_1+W_{other}=K_2+U_2\\\\ U_1=K_2$

The kinetic energy at the bottom equals the gravitational potential energy at the top,

The change in gravitational potential energy depends only on the change in height and is independent of the path,

so the speed at the bottom does not depend on the shape of the ramp.

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