Concept Questions regarding Work

[TJDF]

Homework Statement

Two objects with unequal mass are released from rest from the same height. They slide without friction down a slope and then encounter a rough horizontal region. The coefficient of kinetic friction in the rough region is the same for both masses. The lighter mass will travel further along the rough region before stopping.
True or False?

Homework Equations

Work = Force•displacement•cosθ (angle between force and displacement)
Kinetic Energy = .5•m•v^2
Potential Gravitational Energy: m•g•h

The Attempt at a Solution

The answer is False; but I can't grasp the concept.

 

[LowlyPion]

Homework Statement

Two objects with unequal mass are released from rest from the same height. They slide without friction down a slope and then encounter a rough horizontal region. The coefficient of kinetic friction in the rough region is the same for both masses. The lighter mass will travel further along the rough region before stopping.
True or False?

Homework Equations

Work = Force•displacement•cosθ (angle between force and displacement)
Kinetic Energy = .5•m•v^2
Potential Gravitational Energy: m•g•h

The Attempt at a Solution

The answer is False; but I can't grasp the concept.

Why not?

Write out the equation for what happens.

m*g*h = 1/2*m*v² - u*m*g*d

What happens if you divide the equation by m?

 

[baba89]

This statement is false because the distance traveled by an object is not solely determined by its mass. The force of friction, which is dependent on the coefficient of kinetic friction, will also play a role in determining the distance traveled. The lighter mass may have a smaller force of friction acting on it due to its lower weight, but it will also have a lower amount of kinetic energy to overcome the force of friction. Therefore, the distance traveled by the lighter mass may not necessarily be greater than that of the heavier mass. Additionally, the angle between the force of friction and the displacement may also affect the work done, as seen in the equation for work provided.