Emma is working in a shoe test lab measuring the coefficient of friction for tennis shoes on a variety of surfaces. The shoes are pushed against the surface with a force of 400 N, and a sample of the surface material is then pulled out from under the shoe by a machine. The machine pulls with a force of 300 N before the material begins to slide. When the material is sliding, the machine has to pull with a force of only 200 N to keep the material moving.
a. What is the coefficient of static friction between the shoe and the material?
b. What is the coefficient of dynamic friction between the shoe and the material?
c. Draw a Free Body Diagram for the above.
a. The coefficient of static friction can be calculated using the formula:
Coefficient of static friction = (Force of static friction) / (Normal force)
In this case, the force of static friction is equal to the force applied by the shoe (400 N), and the normal force is also equal to the force applied by the shoe (400 N).
So, the coefficient of static friction = 400 N / 400 N = 1.
b. The coefficient of dynamic friction, also known as kinetic friction, can be calculated using the formula:
Coefficient of dynamic friction = (Force of dynamic friction) / (Normal force)
In this case, the force of dynamic friction is equal to the force applied by the shoe (200 N), and the normal force is still equal to the force applied by the shoe (400 N).
So, the coefficient of dynamic friction = 200 N / 400 N = 0.5.
c. A Free Body Diagram (FBD) for this situation would include the following forces:
- The force of gravity acting vertically downward on the shoe.
- The normal force acting vertically upward on the shoe (equal in magnitude to the force applied by the shoe).
- The force of static friction acting horizontally in the opposite direction of the applied force before the material begins to slide.
- The force of dynamic friction acting horizontally in the opposite direction of the applied force while the material is sliding.
Note: The FBD would also include the forces acting on the material being pulled, but those are not relevant to the questions asked.
a. To calculate the coefficient of static friction, we can use the formula:
Coefficient of static friction (μs) = Force required to start sliding (300 N) / Applied force (400 N)
μs = 300 N / 400 N
μs = 0.75
Therefore, the coefficient of static friction between the shoe and the material is 0.75.
b. To calculate the coefficient of dynamic friction, we can use the formula:
Coefficient of dynamic friction (μd) = Force required to keep sliding (200 N) / Applied force (400 N)
μd = 200 N / 400 N
μd = 0.5
Therefore, the coefficient of dynamic friction between the shoe and the material is 0.5.
c. The Free Body Diagram for the above scenario would include the following forces:
- The applied force (400 N) acting on the shoe in a downward direction.
- The normal force, which is the force exerted by the surface on the shoe in an upward direction, equal in magnitude to the applied force.
- The static frictional force (300 N) acting on the shoe in the opposite direction to the applied force before sliding starts.
- The dynamic frictional force (200 N) acting on the shoe in the opposite direction to the applied force after sliding starts.
Note that these forces should be shown on the Free Body Diagram in their respective directions and magnitudes.
mu static = friction force/normal force = 300/400
similarly
mu dynamic = 200/400
Why are you asking questions that I am sure are covered in your text?