When a spring is stretched by 2 cm, it stores 100J of energy. If it is stretched further by 2 cm, the stored energy will be increased by
Energy is the capacity to perform work, existing in forms like kinetic, potential, thermal, and chemical energy. It is conserved, transforms between types, and powers natural processes and human activities, driving motion, change and technological advancements.
Class 11 Physics Chapter 5, Work, Energy, and Power, explores fundamental concepts such as work done by forces, energy transformations, and power. It covers types of energy, the work-energy theorem, conservation laws, and practical applications, offering a foundation for understanding physical phenomena in mechanics and various real-world contexts.
Share
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.
See More :
https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-5/