Physics: Is a caterpillar turning into a butterfly is or is not a metamorphosis

Is a caterpillar turning into a butterfly is or

Nathanr23

12.10.2020

The momentum is 1.94 kg m/s.

Explanation:

To solve this problem we equate the potential energy of the spring with the kinetic energy of the ball.

The potential energy of the compressed spring is given by

$U = \dfrac{1}{2} kx^2$ ,

where is the length of compression and is the spring constant.

And the kinetic energy of the ball is

$K.E = \dfrac{1}{2}mv^2.$

When the spring is released all of the potential energy of the spring goes into the kinetic energy of the ball; therefore,

$\dfrac{1}{2}mv^2 = \dfrac{1}{2}kx^2,$

solving for we get:

$v = x \sqrt{\dfrac{k}{m} }.$

And since momentum of the ball is p=mv ,

$p =mx \sqrt{\dfrac{k}{m} }.$

Putting in numbers we get:

$p =(0.5kg)(0.25m) \sqrt{\dfrac{(120N/m)}{0.5kg} }.$

$\boxed{p=1.94kg\: m/s}$

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