Question

16
The ball of mass m is thrown with speed v0. The
ball strikes the block of mass 2m and sticks to
it. Find the maximum compression of spring​

Answer 1

Concept:

We need to apply the law of conservation of momentum.

Given:

Mass of ball = m

Speed of ball = v₀

Mass of Block = 2m

Find:

We need to determine the maximum compression of spring

Solution:

Assuming that k is the spring constant

the velocity of the ball having mass 'm' is equal to v₀.

Initially, the '2m' mass of block is at rest.

After the ball of mass m adheres to the block of mass 2m, let the combined system of mass 2m and m move at a velocity of v.

Then, using the law of conservation of linear momentum,

mv₀ + 2m × 0 = (m + 2m)v

or, v = mv₀/3m = v₀/3

We are aware that the energy contained in the spring is provided by if the spring constant is k and the compression is x.

Therefore, E = 1/2kx²

Therefore,

1/2kx² = 1/2 × 3m × (v₀/3)²

kx² = 3m × v₀²/9

x² = v₀²m/3k

Therefore, x = v₀√m/3k

Thus, the maximum compression of spring​ is v₀√m/3k.

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