A student drops a puck, of mass m, from a height h down a frictionless inclined

Question

A student drops a puck, of mass m, from a height h down a frictionless inclined plane. The puck continues a distance d along a horizontal stretch with a coefficient of kinetic friction of U_k, and then goes around a circular loop of radius R.

If the diameter of the loop and the height h are reduced by the same amount (in cm) but the puck still has enough speed to go around the loop, the normal force of the track on the puck at the top of the loop would:

A) Increase
B) Decrease
C) Stay the same.

And reason for choice?

Explanation / Answer

A) Increase

Reason:
By conservation of energy
Total mechanical energy at h = Total mechanical energy at 2R
mgh = mg2R+ 0.5 mv^2 + U_k * m * g *d

now h -2R will remain same

now we can see

normal force = mv^2 /R - mg
V will remain same
but R is reduced so, Normal force should increase

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