Physics Dynamics Friction Problems

Question

43. A 200-lb crate lies on the floor. The coefficient of static friction between the crate and floor is 0.60. What is the minimum force required to start the crate sliding?

44. A 60-kg student sitting on a hardwood floor does not slide until pulled by a 240-N horizontal force. Calculate the coefficient of static friction between the student and the floor.

45. A block rests on an inclined plane. Its angle with the horizontal is increased. When the angle becomes 40 ̊, the block starts to slide. Calculate the coefficient of static friction between the block and the plane.

Answer 1

Before we attempt to answer these, let's review the definition of the coefficient of friction μ. It measures friction between two surfaces in contact.

If two surfaces in contact have a force F_N, in a direction normal to them, then the frictional force, F_f, which acts parallel to the surfaces is given by

F_f = μ. F_N

_{We will use this definition of μ to answer the questions.}

Ques 43: A 200lb crate on the floor exerts a force normal to the surfaces in contact (create & floor). So,

F_N = 200 lbs-force

Note that in this problem, it is not necessary to convert the force units to a specific system (e.g. MKS) unless the question requires it. Your answer for F_f will simply be in the same units as those for F_N.

The minimum force, F_min required to drag the crate parallel to the floor must equal (and just exceed) the Frictional force F_f. Therefore,

F_min = F_f = μ. F_N

Substituting μ=0.6 and F_N = 200lbs

F_f = 120lbs

Ques 44: Here you are given the frictional force (240N) and the normal force (60 Kg). Note that you must have both forces in the same units to calculate μ. Convert weight to Newtons first and then divide F_f with F_N

Ques 45: The picture below shows the various forces acting on the block.

When θ = 40, the force acting to drag the block down is just equal to the force of friction that prevents the block from sliding.

F_f = Mg.Sinθ

The force acting normal to the inclined block surface is

F_N = Mg.Cosθ

By Definition, coefficient of friction

μ = F_f / F_N

You can now calculate μ.