A 218- g block is dropped onto a vertical spring with spring constant k=3.3 N/cm

Question

A 218-g block is dropped onto a vertical spring with spring constant k=3.3 N/cm. The block becomes attached to the spring, and the spring compresses 11.0 cm before momentarily stopping.

A. While the spring is being compressed, what work is done by the block's weight?

B. While the spring is being compressed, what work is done by the spring

C. What was the speed of the block just before it hits the spring?

D. If the speed of impact is doubled, what is the maximum compression of the spring? Assume the friction is negligible.

Explanation / Answer

A) work done by block's weight is W1 = m*g*s = 0.218*9.81*0.11 = 0.2352 J

B) W2 = 0.5*k*x^2 = 0.5*3.3*100*0.11*0.11 = 1.9965 J

C) net work done = change in kinetic energy = 0.5*m*v^2

1.9965-0.2352 = 0.5*0.218*v^2

v = 4.019 m/s

D) Knew is speed is doubled then new kinetic energy is = 0.5*0.218*8.03*8.03= 7.0452 J

then net work done is 0.5*k*x^2 - 0.2352 = 7.0452

0.5*330*x^2 = 7.2804

x = 0.21 m = 21 cm

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