A 700 g block is released from rest at height h 0 above a vertical spring with s

Question

A 700 g block is released from rest at height h0 above a vertical spring with spring constant k = 440 N/m and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring 18.5 cm.

(a) How much work is done by the block on the spring? (in Joules)

(b) How much work is done by the spring on the block? (in Joules)

(c) What is the value of h0? (in meters)

(d) If the block were released from height 2.00h0 above the spring, what would be the maximum compression of the spring? (in cm)

Explanation / Answer

a)

work done by the block on the spring is

W=(1/2)KX2=(1/2)*440*0.1852=7.53 J

b)

Work done by the spring on the block is

W=-7.53 J

c)

By conservation of energy

mgho=-mgx+(1/2)Kx2

.0.7*9.8*ho=-0.7*9.8*0.185+7.53

ho=0.9126 m

d)

now h=2*0.9126=1.825 m

By conservation of energy

0.7*9.8*1.825=-0.7*9.8*x+(1/2)*440*x2

220x2-6.86x-12.52=0

x=0.2546 m

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