A spring, which has a spring constant of 1200 N/m, is compressed x = 0.20 m from

Question

A spring, which has a spring constant of 1200 N/m, is compressed x = 0.20 m
from its equilibrium position with a 5.0 kg block and released at point A. The block travels to
the right along a frictionless track and then up a 15° ramp to a horizontal platform at a height
h = 0.30 m above the base

What is the block’s velocity at point B?

The frictionless ramp is replaced with one that has a rough surface with a kinetic
coefficient of friction of 0.30. The horizontal surfaces are still frictionless. How much
work is done on the block by the frictional force as the block slides up the ramp to the
platform?

With the rough ramp, what is the smallest value of the spring compression that will just
get the block onto the platform?

Explanation / Answer

by conservation of energy

(!/2)kx2 = (!/2)mv2 + mgh

(1/2) x 1200 x0.22 = (1/2) x 5 x v2 + 5 x 9.8 x 0.3

v = 3.72 m/s

when it slides up the platform

work done by friction = mgcos15 x (h/sin15)

W = 16.458 J

for smallest value

(1/2)kx2 = mgh

x = (2mgh/k)

where h = 0.3

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