For given $F - x$ graph, A body of mass $5 k g$ moving with a velocity of $8 m / s$ hits the spring. Calculate the force constant of the spring and also the compression produced in the spring when body hits it.

Open in App

Solution

$F = k x$

$⟹ k = \frac{F}{x} = s l o p e$

$⟹ k = \frac{8}{0.1} = 80 N / m$

The block will continue to compress till the block comes to rest.

From conservation of energy-

$⟹ U_{2} + K_{2} = U_{1} + K_{1}$

$⟹ \frac{1}{2} k x^{2} + 0 = 0 + \frac{1}{2} m v^{2}$

$⟹ x = v \sqrt{\frac{m}{k}}$

$⟹ x = 2 m$

Suggest Corrections

Similar questions

Q. A body of mass

0.1 k g

moving with a velocity of

10 m / s

hits a spring (fixed at the other end) of force constant

1000 N / m

and comes to rest after compressing the spring. The compression of the spring is:

Q. a body of mass 0.1 kg moving with a velocity of 10 m/s hits spring fixed at the other end of force constant 1000 N/m and comes to rest after compressing the spring. the compression of the spring is:

A body of mass 0.1 kg moving with a velocity of 10 m/s hits a spring (fixed at the other end) of force constant 1000 N/m and comes to rest after compressing the spring. The compression of the spring is

Q. A body of mass

0.1 kg

, moving with a velocity of

10 m/s

hits a horizontal spring (fixed at the one end) of force constant

1000 N/m

and comes to rest after compressing the spring. The compression of the spring is,

Q. A body of mass

0.1 kg

moving with a velocity of

10 m/s

hits a spring of force constant

1000 N/m

whose one end is fixed to a wall and comes to rest after compressing the spring. The compression of the spring is

Join BYJU'S Learning Program

For given F−x graph, A body of mass 5kg moving with a velocity of 8m/s hits the spring. Calculate the force constant of the spring and also the compression produced in the spring when body hits it.

F=kx⟹k=Fx=slope⟹k=80.1=80N/mThe block will continue to compress till the block comes to rest.From conservation of energy-⟹U2+K2=U1+K1⟹12kx2+0=0+12mv2⟹x=v√mk⟹x=2m

For given $F - x$ graph, A body of mass $5 k g$ moving with a velocity of $8 m / s$ hits the spring. Calculate the force constant of the spring and also the compression produced in the spring when body hits it.