A block of mass 'm' (as shown in figure) moving with kinetic energy E compresses a spring through a distance 25 cm when, its speed is halved. The value of spring constant of used spring will be nE Nm⁻¹ for n= _________.

Solution

Physics sir · 4 steps

Halve the speed and the kinetic energy drops to a quarter, so the spring stores the missing three quarters.

1. Kinetic energy left. Kinetic energy goes as v². When the speed becomes v/2, the kinetic energy becomes 1/4E.
2. Energy into spring. The surface is smooth, so no energy is lost to friction. The kinetic energy lost, E - E/4 = 3E/4, is stored in the spring.

   1/2kx² = 3E/4

3. Put in numbers. With x = 25 cm = 0.25 m, x² = 1/16 m². So k/32 = 3E/4, which gives k = 24E N m⁻¹.
4. So. k = nE with n = 24.

The common slip: 16. Taking the kinetic energy as halved along with the speed makes the spring store E/2, which gives k = 16E, so n = 16.

The idea to keep. Kinetic energy scales with the square of speed. On a smooth surface, the kinetic energy lost is exactly the elastic energy 1/2kx² gained, so convert x to metres first.

Answer from the NTA final answer key. Solution by PrepWiser.