A spring is resting vertically on a table. A small box is dropped onto the top o

Question

A spring is resting vertically on a table. A small box is dropped onto the top of the spring and compresses it. Suppose the spring has a spring constant of 473 N/m and the box has a mass of 1.4 kg. The speed of the box just before it makes contact with the spring is 0.52 m/s. (a) Determine the magnitude of the spring's displacement at an instant when the acceleration of the box is zero. (b) What is the magnitude of the spring's displacement when the spring is fully compressed?

(a) h = ___ m

(b) h = ___ m

Explanation / Answer

part a )

mg = kx

x = mg/k

x = 0.029 m

part b )

using energy conservation

mghf + kxf^2 = mvo^2/2 + mgho

vertical displacement hf -ho through which the box falls is equal to the displacement of the spring

xf = hf- ho

mvo^2/2 - mg(hf-ho) - kxf^2/2 = 0

kxf^2/2 + mgxf - mvo^2/2 = 0

by solving this quadratic equation

xf = 0.0695 m

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