0. A 3.00-kg block is dropped from rest on a vertical spring whose spring constant is 750 N/m. The block hits the spring, compresses it, and then comes to rest, having fallen through a total vertical distance of 0.45 m. How far is the spring compressed? (Hint: Use conservation of energy.)

the spring compressed is 0.1878 m

Explanation:

Given data

mass = 3 kg

spring constant k = 750 N/m

vertical distance h = 0.45

to find out

How far is the spring compressed

solution

we will apply here law of mass of conservation

i. e

gravitational potential energy loss = gain of eastic potential energy of spring

so we say m*g*h = 1/2 * k * e²

so e² = 2*m*g*h / k

so

we put all value here

e² = 2*m*g*h / k

e² = 2*3*9.81*0.45 / 750

e² = 0.0353

e = 0.1878 m

so the spring compressed is 0.1878 m