Find the Coefficient of Kinetic Friction

[firewareagle]

I have this homework question: A sled is pulled with a horizontal force of 15 N along a level trail, and the acceleration is found to be 0.40 m/s2. An extra mass m = 4.3 kg is placed on the sled. If the same force is just barely able to keep the sled moving, what is the coefficient of kinetic friction between the sled and the trail?

Important equations:
Fk = uk *N
F = ma

Attempt to solve:
Sum of all forces = ma
sum of all forces = Fpull - Fk
Fpull - Fk = ma
Fpull - ma = Fk
Fpull - ma = uk *N
(Fpull - ma)/mg = uk

I'm unable to solve since I don't know what the original mass was, since it says 4.3 extra mass was added. Can someone help me out??

 

[Mordred]

the force and acceleration is given to you use those values to first calculate the mass. essentially your question is two parts the first part is to calculate the original mass using F=ma use that resulatant and add your new mass then calculate the kinetic friction

 

[firewareagle]

right I did that, but i still didn't get the right answer

that way the answer would be 0.0041

but the answer is actually 0.01

 

[Doc Al]

Fpull - Fk = ma

Write two equations: One for before the 4.3 kg mass is added and one for after. You'll have two equations and two unknowns.

 

[rwisz]

I understand your confusion and I would be happy to help you solve this problem. To find the coefficient of kinetic friction, we need to use the equation Fk = uk *N, where Fk is the kinetic friction force, uk is the coefficient of kinetic friction, and N is the normal force.

In this problem, we are given the horizontal force of 15 N and the acceleration of 0.40 m/s2. We also know that the mass of the sled is 4.3 kg. However, we do not know the original mass of the sled. This is okay because we can use the equation F = ma to solve for the original mass.

F = ma
15 N = (m + 4.3 kg) * 0.40 m/s2
15 N = 0.40m + 1.72 kgm/s2
14.28 N = 0.40m
m = 35.7 kg

Now that we have the original mass, we can use it to find the normal force, N. We know that the normal force is equal to the weight of the sled, which is mg. Therefore, N = (35.7 kg + 4.3 kg) * 9.8 m/s2 = 392.6 N.

Now, we can use the equation Fpull - Fk = uk *N to solve for the coefficient of kinetic friction.

Fpull - Fk = uk *N
15 N - Fk = uk * 392.6 N
Fk = 15 N - uk * 392.6 N

We also know that when the sled is just barely able to move, the friction force is equal to the pulling force. Therefore, we can set Fk equal to 15 N and solve for uk.

15 N = 15 N - uk * 392.6 N
uk = 0.04

Therefore, the coefficient of kinetic friction between the sled and the trail is 0.04. I hope this helps you understand how to approach this type of problem. Remember to always use the correct equations and units when solving for a specific variable. Good luck with your homework!