Question #6028a

1 Answer
Jun 17, 2015

Answer:

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.