A 2.50-kg block slides on a horizontal surface with coefficient of kinetic frict

Question

A 2.50-kg block slides on a horizontal surface with coefficient of kinetic friction 0.310. It is moving at 5.45 m/s when it encounters a spring a distance d, at which point it turns around and goes back in the direction it came from, and comes to rest at a distance D beyond the point at which it made contact with the spring.

(a) Find the distance of compression, d.
(b) Find the speed of the block on the return, at the point where it separates from the spring.
(c) Find the distance D beyond the spring where it comes to rest.

Explanation / Answer

A) from work - nergy theorem :

1 x5.45^2 /2 = 0.310 x 2.5g x d + 50d^2 /2

25d^2 + 7.6d - 14.85 = 0

d = 0.63 m

b) 50 x 0.63^2 /2 = 0.31 x g x 0.63 + 1v^2 /2

v = 3.995 m/s

c) 1 x 3.99^2 /2 = 0.310 x 1 x g x d

d = 2.628 m

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