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Chapter 9: Q. 26 (page 228)

A 35-cm-long vertical spring has one end fixed on the floor. Placing a 2.2 kg physics textbook on the spring compresses it to a length of 29 cm. What is the spring constant?

Short Answer

Expert verified

The spring constantk=360N/m

Step by step solution

01

Step 1. Given Information

A vertical spring with 35cm length and a 2.2kg of physics textbook compressed it to a length of29cm

02

Step 2. Hooke's Law

When a spring is compressed, a force is exerted by its material to restore it to its equilibrium position and this force is called restoring force Fsp. Hooke's law state the relationship between the restoring force and the vertical displacement ∆y

Fsp=-k∆y

where kis the force constant and the negative sign shows the direction

03

Step 3. Find the spring constant

The book presses against the free end of the spring, so it exerts a force in the negative sign of the restoring due to its weight mg, so the force is given by

F=Fspmg=-k∆yk=-mg∆y

the length of the spring changes from 35cm to 29cm, we put the values

k=-mg∆y=(2.2kg)(9.8m/s2)0.29m-0.35m=360N/m

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