Question

A woman holding a large rock stand on a frictionless,horizontal sheet of ice. She throws the rock with speed at anangleabove the horizontal. Consider the system consisting of thewoman plus the rock. Is the momentum of the system conserved?Why or why not? Is any component of the momentum of thesystem conserved? Again, why or why not?

Short answer

The external forces are acting on the system, so the momentum of the system is not conserved.

There is no friction or any other external forces in the horizontal direction. Therefore, the horizontal component of momentum is conserved.

Step-by-step solution

Conservation of momentum:

If the net external force acting on a system is zero, the total momentum of the system$\overrightarrow{\mathbf{P}}$ (the vector sum of the momenta of the individual particles that make up the system) is constant or conserved.

If$\mathbf{\sum }_{\mathbf{}}\overrightarrow{\mathbf{F}}\mathbf{=}\mathbf{0}$

Then

$\overrightarrow{\mathbf{P}}$= constant

Discussion.

There are two external forces on the system in the vertical direction one is gravity, which is directed downward, and the other is the normal force due to contact of ice with the surface which is directed upward.

When the woman is standing these forces cancel each other but after she throws the rock at a certain angle with velocity. There will be a component acting downward.

Since the external forces are acting on the system so total momentum of the system is not conserved.

Since there is no friction or any other external forces in the horizontal direction. Therefore, the horizontal component of momentum is conserved.