A 834 g block is released from rest at height h0 above a vertical spring with sp

Question

A 834 g block is released from rest at height h0 above a vertical spring with spring constant k = 260 N/m and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring 18.9 cm. How much work is done (a) by the block on the spring and (b) by the spring on the block? (c) What is the value of h0? (d) If the block were released from height 5h0 above the spring, what would be the maximum compression of the spring? Number Units Number Units Number Units Number Units

Explanation / Answer

a) w = 0.5*k*x^2 = 0.5*260*0.189*0.189 = 4.64 J

b) W = -4.64 J

c) W = m*g*ho + m*g*x

ho = 0.38 m

d)

TEi = m*g*5ho + m*g*x

TEf = 0.5*k*x^2

0.5*k*x^2 = m*g*5ho + m*g*x

(0.5*260*x^2) = (0.834*9.8*5*0.38)+(0.834*9.8*x)

130x^2 - 8.1732x -15.52908 = 0

x = 0.378m   (0.38 m nearly) = 37.8 cm = 38 cm

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