Question #6028a

Question

2007 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-17T10:04:14

The steel ball will have a higher momentum.

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

$p = m \cdot v$ $p = m * v$ , where

$p$ $p$ - momentum;
$m$ $m$ - the mass of the object;
$v$ $v$ 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

$p_{steel} = m_{steel} \cdot v$ $p_"steel" = m_"steel" * v$

and

$p_{cotton} = m_{cotton} \cdot v$ $p_"cotton" = m_"cotton" * v$

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.