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 250 N/m and the box has a mass of 2.6 kg. The speed of the box just before it makes contact with the spring is 0.33 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= _______

(b) h= ________

Explanation / Answer

Here ,

spring constant , k = 250 N/m

mass of box , m = 2.6 Kg

speed of block , u = 0.33 m/s

a)

for the zero acceleration of the box

m * g = k * x

2.6 * 9.8 = 250 * x

x = 0.102 m

the magnitude of the spring’s displacement at an instant when the acceleration of the box is zero is 0.102 m

b)

for the spring to be fully compressed

displacement is x

using conservation of energy

0.5 * k * x^2 = m * g * x + 0.5 * m * v^2

0.5 * 250 * x^2 = 2.6 * 9.8 * x + 0.5 * 2.6* 0.33^2

sovling for x

x = 0.209 m

the magnitude of the spring’s displacement when the spring is fully compressed is 0.209 m

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