Question

A 2.14 kg block resting on a frictionless surface is attached to an ideal spring with spring constant k = 252 Nm . The block is pushed to compress the spring by 9.08 cm from its equilibrium position. While the spring is being compressed, find (a) the work done by the spring and (b) the work done by the applied force.

Answer 1

1.03882464 Joules

2.07764928 Joules

Step-by-step explanation:

k = Spring constant = 252 Nm

x = Distance compressed = 0.0908 m

Potential energy of the spring

`P=(1)/(2)kx^2\\\Rightarrow P=(1)/(2)* 252* 0.0908^2\\\Rightarrow P=1.03882464\ J`

Work done by the spring is 1.03882464 Joules

Force on spring

`F=kx\\\Rightarrow F=252* 0.0908\\\Rightarrow F=22.8816\ N`

Work done

`W=F* s\\\Rightarrow W=22.8816* 0.0908\\\Rightarrow W=2.07764928\ J`

Work done by the applied force is 2.07764928 Joules