Question

Ball of mass m thrown with speed V not strikes a block of mass 2m and sticks to it find the maximum compression of spring

Answer 1

Answer:

$x=v_0\sqrt{\frac{m}{3k}}$

Explanation:

Assuming the spring constant to be k

velocity of the ball of mass m = v₀

The ball of mass 2m is in rest initially

Let the velocity of the combined system of mass 2m and m be v after the ball of mass m sticks to the block of mass 2m

Then,

Using the principle of conservation of linear momentum

mv₀ + 2m × 0 = (m + 2m)v

or, v = mv₀/3m = v₀/3

We know that if the spring constant is k and and compression is x then the energy stored in the spring is given by

$\boxed{E=\frac{1}{2}kx^2}$

Thus

$\frac{1}{2}kx^2}=\frac{1}{2}\times 3m\times(\frac{v_0}{3})^3$

$\implies kx^2=3m\times\frac{v_0^2}{9}$

$\implies x^2=\frac{v_0^2m}{3k}$

$\implies x=v_0\sqrt{\frac{m}{3k}}$

Hope this is helpful.

Answer 2

Answer:see the attachment

Good luck

Explanation: