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 FBD for the above.
To find the coefficient of static friction (µs), we can use the formula:
µs = Fs / N
where Fs is the force required to start the sliding motion, and N is the normal force.
In this case, the force required to start the sliding motion is 300 N, and the normal force is equal to the force with which the shoes are pushed against the surface, which is 400 N.
Therefore, µs = 300 N / 400 N, which simplifies to µs = 0.75.
So, the coefficient of static friction between the shoe and the material is 0.75.
To find the coefficient of dynamic friction (µd), we can use the formula:
µd = Fd / N
where Fd is the force required to keep the material moving, and N is the normal force.
In this case, the force required to keep the material moving is 200 N, and the normal force is still 400 N.
Therefore, µd = 200 N / 400 N, which simplifies to µd = 0.5.
So, the coefficient of dynamic friction between the shoe and the material is 0.5.
To draw a free body diagram (FBD), we need to consider the forces acting on the system. In this case, the forces acting on the system are:
1. Normal force (N) acting perpendicular to the surface, which is equal to the force with which the shoes are pushed against the surface (400 N).
2. Force of gravity (mg) acting downwards, where m is the mass of the shoe and g is the acceleration due to gravity.
3. Force of static friction (Fs) acting parallel to the surface, opposing the applied force.
4. Force of dynamic friction (Fd) acting parallel to the surface, opposing the applied force.
Note that the normal force and force of gravity cancel each other out vertically, so we only need to show the forces acting horizontally.
The FBD would look like this:
N (400 N)
-------------------------
|||
||| <- Force of static friction (Fs)
|||
||| <- Force of dynamic friction (Fd)
|||
|||
-------------------------
Please note that the actual arrows in the FBD should be labeled with the corresponding magnitudes and directions of the forces acting on the system.