A block of mass m travelling at a speed v compresses a spring by a distance x before its speed reduces to half. Determine the spring constant of the spring.

Step-by-step solution

According to the law of conservation of mechanical energy, the decrease in kinetic energy of the block is equal to the potential energy stored in the spring. Initial kinetic energy of the block is K_i = 1 2 mv^2 Final kinetic energy of the block is K_f = 1 2 m ( v 2 )^2 = 1 8 mv^2 Potential energy stored in the spring is U = 1 2 kx^2 Equating the change in kinetic energy to the potential energy: K_i - K_f = U 1 2 mv^2 - 1 8 mv^2 = 1 2 kx^2 3 8 mv^2 = 1 2 kx^2 k = 3mv^2 4x^2