A 350-g block is dropped onto a relaxed vertical spring that has a spring consta

Question

A 350-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 60.3 cm before momentarily stopping. While the spring is being compressed, What work is done on the block by the gravitational force on it? While the spring is being compressed, What work is done on the block by the spring force? What is the speed of the block just before it hits the spring? (Assume that friction is negligible.) If the speed at impact is doubled, What is the maximum compression of the spring?

Explanation / Answer

PART A

mass of block , m = 0.35 Kg

k = 100 N/m

x = 60.3 cm = 0.603 m

work done by gravitational force = m * g * x

work done by gravitational force = 0.35 * 9.8 * 0.603 J

work done by gravitational force = 2.07J

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PART B

work done by the spring force = - 0.5 * k * x^2

work done by the spring force = - 0.5 * 100 * 0.603^2

work done by the spring force = -18.18 J

PART C

let the speed of the block is v

Using conservation of energy

0.5 * 0.35 * v^2 = - 2.07 + 18.18

v = 9.59 m/s

-----------------------------------------

PART D

let the compression is x

for double the speed

0.5 * 200 * x^2 - m * g * x = 0.5 * 0.35 * (2 * 9.59)^2

0.5 * 200 * x^2 - 0.35 * 9.8 * x = 0.5 * 0.65 * (2 * 11.8)^2

solving for x

x = 0.97 m

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