Mechanical Energy dissapation

[ViewtifulBeau]

The figure above shows three choices for the orientation of a plane that is not frictionless, and for the direction in which a block slides along the plane. The block begins with the same speed in all three choices, and slides until the kinetic frictional force has stopped it. For which choice is the amount of mechanical energy dissipated greatest?

The first figure is of a block on a horizontal plane.
The second figure is of a block on a sloped plane and the block's original velocity was down the slope.
The third figure is of a block on the same sloped plane, but the initial velocity was up the slope.

I thought the answer was the third figure, but it isn't. Now I think that all of the energy dissapated is equal because they all come to a stop. So all of the energy is gone. (but don't they stop at different times?) thanks

 

[FluxCapacitator]

Here's a hint, there's energy in many forms, kinetic, heat, and of course, gravitaitonal.

 

[quicknote]

You are correct that all of the energy is dissipated in all three scenarios, as the block comes to a stop in all three cases. However, the amount of mechanical energy dissipated may not be equal in all three cases. This is because the amount of mechanical energy dissipated is dependent on the distance the block travels and the force of friction acting on it.

In the first figure, the block slides along a horizontal plane, meaning that it travels the shortest distance before coming to a stop. This results in the least amount of mechanical energy being dissipated.

In the second figure, the block slides down a sloped plane, meaning it travels a greater distance before coming to a stop. Additionally, the force of friction acting on the block is greater due to the slope, resulting in more mechanical energy being dissipated compared to the first figure.

In the third figure, the block initially travels up the slope, meaning it travels the greatest distance before coming to a stop. However, the force of friction acting on the block is in the opposite direction of its motion, resulting in less mechanical energy being dissipated compared to the second figure.

So, in conclusion, the amount of mechanical energy dissipated is greatest in the second figure, where the block slides down the sloped plane with an initial velocity in the same direction as the force of friction. This is because both the distance traveled and the force of friction contribute to the dissipation of mechanical energy.