A 292 g block is dropped onto a relaxed vertical spring that has a spring consta

Question

A 292 g block is dropped onto a relaxed vertical spring that has a spring constant of k cm before momentarily stopping. 2.0 N/cm. The block becomes attached to the spring and compresses the spring 14 (a) While the spring is being compressed, what work is done on the block by the gravitational force on it? (b) What work is done on the block by the spring force while the spring is being compressed? (c) What is the speed of the block just before it hits the spring? (Assume that friction is negligible.) m/s (d) If the speed at impact is doubled, what is the maximum compression of the spring?

Explanation / Answer

here,

mass , m = 292 g = 0.292 kg

spring constant , K = 2 N/cm = 200 N/m

compression in the spring , x = 12 cm = 0.14 m

a)

the work done on the block by the gravitational force , Wg = m * g * x

Wg = 0.292 * 9.81 * 0.14 J

Wg = 0.4 J

b)

the work done by the spring , Ws = 0.5 * K * x^2

Ws = 0.5 * 200 * 0.14^2 J

Ws = 1.96 J

c)

let the initial speed of block be u

using work energy theorm

Ws - Wg = 0.5 * m * u^2

1.96 - 0.4 = 0.5 * 0.292 * u^2

solving for u

u = 3.27 m/s

d)

when the initial speed is doubled

u' = 2 * u = 6.54 m/s

let the compression of the spring be x'

using work energy theorm

Ws - Wg = 0.5 * m * u'^2

0.5 * K * x'^2 - m * g * x' = 0.5 * m * u'^2

0.5 * 200 * x'^2 - 0.292 * 9.81 * x' = 0.5 * 0.292 * 6.54^2

solving for x'

x' = 0.26 m

the compression in the spring is 0.26 m

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