A 575-g block is dropped onto a relaxed vertical spring that has a spring consta

Question

A 575-g block is dropped onto a relaxed vertical spring that has a spring constant k-100.0 N/m. The block becomes attached to the spring and compresses the spring 81.7 cm before momentarily stopping. While the spring is being compressed, what work is done on the block by the gravitational force on it? Submit Answer Tries 0/6 While the spring is being compressed, what work is done on the block by the spring force? Submit Answer Tries 0/6 What is the speed of the block just before it hits the spring? (Assume that friction is negligible.) Submit Answer Tries 0/6 If the speed at impact is doubled, what is the maximum compression of the spring? Submit Answer Tries 0/6

Explanation / Answer

Work done by gravitational force

W = m g h = 0.575 x 9.81 x 0.817

W = 4.61 J ........Ans

Wspring = k d^2 /2 = (100) (0.817^2) / 2

= - 33.4 J .......Ans

Work done by spring + work done by gravity = changein KE

-33.4 + 4.61 = 0 - 0.575 v^2 /2

v = 10 m/s ........Ans

Applying work - energy theorem,

(0.575 x 9.81 x d) - (50 d^2) = 0 - (0.575 x 20^2 / 2)

50 d^2 - 5.64 d - 115 = 0

d = 1.57 m .........Ans

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