In moving a 35.0 kg desk from one side of a classroom to the other, a professor finds that a horizontal force of 300 N is necessary to set the desk in motion, and a force of 185 N is necessary to keep it in motion at a constant speed.
(a) What is the coefficient of static friction between the desk and the floor?
(b) What is the coefficient of kinetic friction between the desk and the floor?
I know that F=ma, but how do you do this?
You don't use F = ma. The desk is not accelerating. All that equation tells you is that the pusing force is equal to the opposiing friction force. The net force on the desk is zero.
The static coefficient of friction is 300N/(M g)
The kinetic coefficient of friction is
185/(M g)
Note that the denominator is the weight, not the mass.
Plug in for mass M and g (the acceleration of gravity) and crank away.
Thanks!
To solve this problem, you can use the relationship between the applied force, frictional force, and the weight of the object. Here's how you can find the coefficients of static and kinetic friction:
(a) To determine the coefficient of static friction, we need to calculate the maximum force of static friction that is required to set the desk in motion. This can be found using the formula:
Fs(max) = μs * N
Where Fs(max) is the maximum force of static friction, μs is the coefficient of static friction, and N is the normal force acting on the desk.
In this case, we know the applied force required to set the desk in motion, which is 300 N. We will assume that the normal force acting on the desk is equal to its weight, which can be calculated by multiplying the mass of the desk (35.0 kg) by the acceleration due to gravity (9.8 m/s²):
N = m * g = 35.0 kg * 9.8 m/s²
Now, we can rearrange the formula to solve for the coefficient of static friction:
μs = Fs(max) / N
Substituting the values, we get:
μs = 300 N / (35.0 kg * 9.8 m/s²)
Now you can calculate the coefficient of static friction.
(b) To find the coefficient of kinetic friction, we use a similar approach. The force required to keep the desk moving at a constant speed is equal to the force of kinetic friction:
Fk = μk * N
Where Fk is the force of kinetic friction, μk is the coefficient of kinetic friction, and N is the normal force.
From the given information, the applied force required to keep the desk in motion is 185 N. Again, we will assume that the normal force acting on the desk is equal to its weight. Using the same formula as before, we can find the coefficient of kinetic friction:
μk = Fk / N
Substituting the values, we get:
μk = 185 N / (35.0 kg * 9.8 m/s²)
Now you can calculate the coefficient of kinetic friction.
Using these formulas, you can find the coefficients of static and kinetic friction by plugging in the given values and calculating the final result.