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?