Question

a solid of mass 2kg moving with velocity 10 m/s strikes an ideal weightless spring and produces a compression of 25 cm in it. calculate the force constant of the spring.

Answer 1

3200N/m
1/2mv2 = 1/2Kx2

Answer 2

Answer:

3200 N/m

Explanation:

When the solid mass of mass 2 kg strikes the spring with a velocity of 10 m/s, its kinetic energy get changed into the potential energy in the spring on compressing 25 cm.

So, the loss in kinetic energy will be equal to the gain in potential energy in the spring.

$\therefore \dfrac{1}{2}mv^2=\dfrac{1}{2}kx^2\\\Rightarrow mv^2=kx^2\\\Rightarrow k=\dfrac{mv^2}{x^2}\\\Rightarrow k=\dfrac{2\ kg\times (10\ m/s)^2}{(0.25\ m)^2}\\\Rightarrow k= 3200\ N/m$

Hence, the force constant of the spring is 3200 N/m.