Question

Answer it:

If a spring is compressed 2.0cm with respect to its equilibrium position and then compressed another 2.0cm, how much more work is done in the second compression than in the first? Explain

Answer 1

The work done in compressing a spring a further 2.0 cm after the first 2.0 cm is three times the work done in the first compression because the work depends on the square of the displacement.

Step-by-step explanation:

When a spring is compressed from its equilibrium position, the work done on it is given by the equation W = ½kx², where k is the spring constant and x is the displacement from equilibrium.

Compressing the spring by 2.0 cm (which we can call x) and then another 2.0 cm (for a total of 4.0 cm or 2x), the work done during the second compression can be calculated as the difference in work between compressing the spring from 0 to 4.0 cm and 0 to 2.0 cm.

Using the relationship W = ½kx²,

we know that W(0 to 4.0 cm) is four times W(0 to 2.0 cm), meaning W(2.0 cm to 4.0 cm) = 3W(0 to 2.0 cm).

Thus, the work done in the second compression is three times more than the work done in the first.