52 A 250g block is dropped onto a relaxed vertical spring that has a spring cons

Question

52 A 250g block is dropped onto a relaxed vertical spring that has a spring constant of k = 2.5 Nicm (Fig. 7-38). The block be comes attached to the spring and compresses the spring 12cm be- fore momentarily stopping. While the spring is being compressed, what work is done on the block Fig.7-38 Problem 52. by (a) the gravitational force on it and (b) the spring force? (c) What is the speed of the block just before it hits the spring?(Assume that friction is negligi- ble.) (d) If the speed at impact is doubled, what is the maxi- mum compression of the spring?

Explanation / Answer

(a)
Work Done = mgh = 0.25*9.8*0.12 = 0.294 J

(b)
Spring Force = -kx = -2.5*0.12 = 0.3 N

(c)
1/2kx^2 = 1/2mv^2
2.5*12^2 = 0.25*v^2
v = (1440)^(1/2)
v = 37.95 m/s

(d)
1/2kx^2 = 1/2mv^2
2.5*x^2 = 0.25*(37.95*2)^2
x = 24 cm

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