(a) A block of wood is pushed against a spring, which is compressed 0.080 m. Does the force on the block exerted by the spring do positive or negative work? Does the potential energy stored in the spring increase or decrease? (b) A block of wood is placed against a vertical spring that is compressed 6.00 cm. The spring is released and pushes the block upward. From the point where the spring is compressed 6.00 cm to where it is compressed 2.00 cm from its equilibrium length and the block has moved 4.00 cm upward, does the spring force do positive or negative work on the block? During this motion, does the potential energy stored in the spring increase or decrease?

• The compression is$0.080$.

If a body is subjected to deformation, and it returns to its original shape and size after the deformation then the body is said to be elastic. The deformable bodies such as springs or rubber bands stored the energy in the form of elastic potential energy.

The elastic potential energy is given by,

${\mathrm{U}}_{\mathrm{el}}=\frac{1}{2}{\mathrm{kx}}^2$

Where k is the spring constant and x is the displacement from the relaxed position.

When the spring is compressed, the spring tries to return the block to its original position. So, the force exerted by the spring on the block is opposite to the displacement of the block.

Therefore, work done by the spring force is negative.

The work done against the spring force is stored in the form of elastic potential energy. The stored potential energy will be more when the spring is compressed or stretched more from the original position. So, the potential energy stored in the spring increases when the spring is compressed. This can also be observed from the expression for elastic potential energy.

Therefore, the potential energy stored in the spring increases when the spring is compressed.

The block moves a vertical distance of$4.00\mathrm{cm}$and all along this path, the spring is pushing the block in the upward direction. In this case, the spring force and the displacement both are in the same direction.

Therefore, the work done by the spring force is positive.

The spring will have some stored energy when it is compressed, and the spring does work at the expense of this stored energy. So, the spring has displaced the block$4.00\mathrm{cm}$at the expense of its potential energy, and hence the potential energy stored in the spring decreases. This can be observed from the expression for elastic potential energy.

The$\mathrm{x}$was 6 00 cm initially and finally, it became 4 00 cm, thereby suggesting a decrease in potential energy.

Therefore, the energy stored in the spring will decrease.