Question

Question #6028a

Answer 1

The steel ball will have a higher momentum.

Explanation:

Momentum depends on the velocity and on the mass of an object according to the following relationship

`p = m * v`, where

`p` - momentum;
`m` - the mass of the object;
`v` the velocity of the object.

In your case, you know that the speed of the steel ball is equal to the speed of the cotton ball, so you can write

`p_"steel" = m_"steel" * v`

and

`p_"cotton" = m_"cotton" * v`

You can establish a relationship between the momentum of the steel ball and the momentum of the cotton ball by dividing these two equations

`p_"steel"/p_"cotton" = m_"steel"/m_"cotton" * cancel(v)/cancel(v)`

However, you have no information about the masses of the two balls, but you know something about their volumes.

Mass can be expressed by using density and volume

`rho = m/V => m = rho * V`

Since you know that the two balls have equal volumes, you can write

`p_"steel"/p_"cotton" = (rho_"steel" * cancel(V))/(rho_"cotton" * cancel(V))`

`p_"steel"/p_"cotton" = rho_"steel"/rho_"cotton"`

Since the density of steel is bigger than the density of cotton, you have

`p_"steel" = underbrace(rho_"steel"/rho_"cotton")_(color(blue)(">0")) * p_"cotton"`

Therefore, the steel ball will have the greater momentum if velocity and volume are equal.