What is going on here? - Mechanics Puzzler

[emob2p]

A boat is moving in the x-direction with constant velocity. The frictional force against the boat is constant and independent of its mass. There is a pile of sand on the boat. Someone starts shoveling the sand off the boat strictly in the y-direction with respect to the boat.
Here is my question:
If the frictional force is independent of the boat's mass, then the forces in the x-direction (force of engine + frictional force) should always cancel regardles off the sand being shoveled off. But at the same time, dp/dt in the x-direction should not be zero because the boat's mass is changing even though the mass is being shoveled off in the y-direction. How to resolve this problem?

 

[member 553083]

How can the force still be constant even though the mass is changing?The answer to your question is that the frictional force is independent of the boat's mass, but it is not necessarily constant. As the mass of the boat changes due to the sand being shoveled off, so does the frictional force. The net force in the x-direction (force of engine + frictional force) will therefore not remain constant as the mass of the boat changes.

 

[wais]

It seems like there may be a misunderstanding about the concept of frictional force in this scenario. Frictional force is not independent of the boat's mass, but rather it is independent of the boat's velocity. This means that the force of friction will remain constant regardless of how much sand is on the boat or how much is being shoveled off.

In this scenario, the boat's velocity in the x-direction is constant, which means that the forces in the x-direction (engine and friction) are balanced. However, when the sand is being shoveled off in the y-direction, there is a change in the boat's mass in the x-direction. This change in mass will result in a change in the boat's momentum in the x-direction, causing a non-zero value for dp/dt in that direction.

To resolve this problem, we must take into account the change in mass and momentum in the x-direction due to the sand being shoveled off. This could be calculated using the equation F=ma, where a is the acceleration in the x-direction caused by the change in mass.

Overall, the key concept to remember is that frictional force is not independent of mass, but rather velocity. And in this scenario, the change in mass due to the shoveling of sand will have an effect on the boat's momentum in the x-direction.