Spring Problem A 10.0kg stone slides down a snow-covered hill, leaving point A w

Question

Spring Problem

A 10.0kg stone slides down a snow-covered hill, leaving point A with a speed of 5.00m/s. There is no friction on the hill between points A and B, but there is friction on the level ground at the bottom of the hill, between B and the wall. Speed of the rock when it is reaching B is 25.0 m/s. After entering the rough horizontal region, the stone travels 100 m and then runs into a very long, light spring with force constant 5.00N/m. The block stops when the spring is compressed by 10.0 m.

a) What is the height of the hill H?

b) What is the restoring force of the spring acting on the rock when it stops?

c) If the coefficient of static friction between the block and the surface is 0.600, what is the magnitude of the force of static friction acting on the rock when it stops?

d) What is the kinetic friction coefficient between the surface and the rock?

Explanation / Answer

a) let the height of the mountain be h.so conserving eenergy,

0.5 mu^2+ mgh =0.5mv^2

or 0.5*5^2 +9.81*h=0.5*25^2

or h=30.581 m

b) force= k*x

=5*10

=50 N

c) frictional force = umg

=10*9.81*10

=981 N

d) let the force be f.so conserving energy,

0.5mv^2 = f.x + 0.5 kx^2

or 0.5*10*25^2 = f*110 + 0.5*5*10^2

or f=26.13 N

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