Physics question

Question

a 2.25-kg block is released from rest on a ramp of height h. When the block is released, it slides without friction to the bottom of the ramp, and then continues across a surface that is frictionless except for a rough patch of width 15.0 cm that has a coefficient of kinetic friction 𝜇_k = 0.660. Find h such that the block's speed after crossing the rough patch is 3.80 m/s

Answer 1

The friction on the patch of length L = 0.15 m does negative work W_friction = - µmgL, which decreases the mechanical energy (kinetic + potential):

K_i + U_i + W_friction = K_f + U_f

0 + mgh - µmgL = mv²/2 + 0

h = µL + v²/(2g)

Plug in values. The mass m cancels out and the answer does not depend on it.