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Question

A cart rolls halfway down a flat, frictionless ramp so that none of the mechanical energy (kinetic plus potential) is lost. How much speed does the cart have halfway down(v1), compared to how much it will have at the bottom (v2)?

A
v1=0.5v2
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B
v1<0.5v2
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C
0.5v2<v1<0.75v2
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D
v1=0.25v2
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E
v1=0.75v2
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Solution

The correct option is C 0.5v2<v1<0.75v2
The total mechanical energy is conserved,
Let the speed halfway down be v1 and that at the bottom be v2.
Speed halfway down is given by

12mv21=mgh

v1=2gh
The speed at the bottom is given by-

12mv22=mg(2h)

v2=4gh
v2=2v1

v1=v220.707v2

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