Hooke\'s law describes a certain light spring of unstretched length 36.0 cm. Whe

Question

Hooke's law describes a certain light spring of unstretched length 36.0 cm. When one end is attached to the top of a door frame and a 5.40-kg object is hung from the other end, the length of the spring is 40.0 cm.

A. Find its spring constant.
           ____________ kN/m
            
B. The load and the spring are taken down. Two people pull in opposite directions on the ends of the spring, each with a force of 200 N. Find the length of the spring in this situation.
                ____________ m

Explanation / Answer

Here ,

change in length of spring , x = 40 - 36

x = 4 cm = 0.04 m

A. for the spring constant

spring force = m * g

k * 0.04 = 5.4 * 9.8

k = 1323 N/m

k = 1.323 kN/m

the spring constant is 1.323 kN/m

B)

for force = 200 N

200 = 1323 * x

x = 0.151 m

x = 15.1 cm

the length of spring = 36 + 15.1

the length of spring = 51.2 cm

the the length of spring is 51.2 cm

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