Question

A block of mass m moving at a speed v Compresses a spring through a distance x before its speed is halved. Find the spring constant of the spring.
Concept of Physics - 1 , HC VERMA , Chapter " Work and Energy"

Answer 1

Let the velocity at starting is v.

After compression change in velocity = v/2
Here , Initial Kinetic energy of a block = (1/2)mv²

After compression of spring,
Total energy at the point x = Kinetic energy of a block + Potential Energy which stored in the spring.

 1/2 (mv²) = 1/2 m(v/2)² + 1/2 kx²
1/2 kx² = 1/2 m(v/2)² - 1/2 (mv²)
kx² = m { v² - v²/4} )
kx² = 3mv² /4

$k = 3mv^2 / 4x^2$ . 

Hence k ( spring constant ) is equal to = 3mv² / 4x²

Hope it Helps. :-)

Answer 2

Answer:3mv^2/4x^2

Explanation: