When a spring is stretched, the energy stored in it is given by the formula for elastic potential energy, which is proportional to the square of the displacement from its equilibrium position. If the spring is initially stretched by 2 cm and stores 100 J of energy, stretching it further by another 2 cm results in a total stretch of 4 cm.

The energy stored in the spring at any stretch can be expressed as follows:
1. For the first stretch of 2 cm:
Energy = k ⋅ (2²) = k ⋅ 4 (where k is the spring constant)
2. For the total stretch of 4 cm:
Energy = k ⋅ (4²) = k ⋅ 16

The increase in energy when stretched from 2 cm to 4 cm can be calculated as follows:

– Total energy at 4 cm: k .16
– Initial energy at 2 cm: k . 4

The increase in energy will then be:

– Increase in energy = k . 16 – k . 4 = k . 12

Given that k⋅4 = 100 J, we know that the total energy stored at 4 cm is 4⋅ 100 = 400 J.

Hence, the amount of increase in the energy stored when the spring is stretched further by 2 cm is: 300 J.

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