6. Thomas sits on a small rug on a polished wooden floor. The coefficient to kinetic friction between the rug and the slippery wooden floor is only 0.12. If Thomas weighs 650 N, what horizontal force is needed to pull the rug

and Thomas across the floor at a constant speed?[78N]

1

F=78 N

Explanation:

Taking to Thomas and the rug as a single system, if they slide across the floor at constant speed, this means that their acceleration is just zero.According to Newton's 2nd Law, if the acceleration is zero, this means that the net force applied is zero too.In the horizontal direction, there are two forces acting on Thomas and the rug (as a single system), the applied force, and the kinetic friction force, which must be equal and opposite each other:

     

By definition, as the friction force is the horizontal component of the contact force, it can be expressed as follows:

     

     where μk = coefficient of kinetic friction = 0.12

     Fn = normal force

In this case, as the system boy+rug is not accelerating in the vertical direction, and the surface is level, the normal force (which is always perpendicular to the surface), must be equal to the force of gravity.Assuming that the mass of the rug is neglectable, we can write:

     

Replacing (3) and μk in (2)

     

From (1), we finally get: