Help finding coefficient of kinetic friction

In summary, a box slides down a 30.0 degree ramp with an acceleration of 1.20m/s^2. The coefficient of kinetic friction between the box and the ramp is .44.
  • #1
Deathchariot
3
0
"A box slides down a 30.0 degree ramp with an aceleration of 1.20m/s^2. Determine the coefficient of kinetic friction between the box and the ramp."

I know that the coefficient of kinetic friction is found by kinetic friction / normal force, but the only problems I've delt with in the past gave you the mass of the object. In those cases, I would find the force of gravity then use it to find the force upwards using the sin of the angle of the incline. From there, I would find the normal force subtracting force upwards from the force of gravity - then finally multiplying the mass times the acceleration to find the kinetic friction.

I know how to work through it one way, but I can't figure out how to work backwards given the acceleration and no mass. Could someone please point me in the right direction?
 
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  • #2
Call the mass "m" and work it out just as you would if you had the mass. You'll find that in every equation you'll need, the mass will drop out. Try it.
 
  • #3
So I have force of gravity = m (9.81m/s^2)

Force upwards = m(9.81m/s^2)sin30
Force upwards = m(4.905)

Normal force = Fg - Fup
Normal force = m(9.81m/s^2) - m(4.905)
Normal force = m(4.905)

then I lose myself - I'm not sure if I'm on the track that you mean...
 
  • #4
Deathchariot said:
So I have force of gravity = m (9.81m/s^2)

Force upwards = m(9.81m/s^2)sin30
Force upwards = m(4.905)

Normal force = Fg - Fup
Normal force = m(9.81m/s^2) - m(4.905)
Normal force = m(4.905)

then I lose myself - I'm not sure if I'm on the track that you mean...


Do you think you could just forget about the numbers and just work out the math to the end, and you should end up with an expression for the coefficient of kinetic friction. I mean forget about numerical stuff until the very end, just call gravity g, mass m, acceleration a etc etc...
 
  • #5
in a ramp, if there was no friction, then the accelration would be 9.8m/s^2?
i would guess then..with friction
[tex] \mu_{k} = \frac{F_{fr}}{F_n}
\\ = \ \frac{(mg-ma}{mg-\sin(\theta)mg}
[/tex]

is the above correct? I am a HS student too..

or...wait..i messed up the normal force...
 
Last edited:
  • #6
First tip: Don't plug numbers in until the end--use symbols.

There are three forces acting on the block:
(1) the weight (mg) which acts vertically down
(2) the normal force (what is that?) which acts normal to the surface
(3) the friction force ([itex]\mu N[/itex]) which acts up the ramp

Find the components of the weight parallel and perpendicular to the ramp. Then use that to find the normal force. Then use Newton's 2nd law for force components parallel to the ramp. (That's when you'll write an equation and the mass with cancel out. You'll solve that equation for [itex]\mu[/itex].)
 
  • #7
Thanks for all of the help, Doc Al - I finally got an answer of .44!
 
Last edited:

1. What is the coefficient of kinetic friction?

The coefficient of kinetic friction is a measure of the amount of resistance between two surfaces in contact when one of the surfaces is in motion. It is represented by the symbol μk and is a dimensionless quantity.

2. How do I find the coefficient of kinetic friction?

The coefficient of kinetic friction can be found by dividing the force of kinetic friction by the normal force between the two surfaces. The force of kinetic friction can be calculated by multiplying the coefficient of kinetic friction by the normal force.

3. What affects the coefficient of kinetic friction?

The coefficient of kinetic friction is affected by factors such as the roughness of the surfaces, the materials of the surfaces, and the presence of any lubricants or contaminants. It also depends on the force with which the surfaces are pressed together.

4. Can the coefficient of kinetic friction be greater than 1?

Yes, the coefficient of kinetic friction can be greater than 1. This indicates a high amount of resistance between the two surfaces in motion. However, it is not common for the coefficient of kinetic friction to be greater than 1.

5. Why is the coefficient of kinetic friction important?

The coefficient of kinetic friction is important in understanding and predicting the motion of objects on surfaces. It helps in determining the amount of force required to move an object, as well as the acceleration and speed of the object. It is also important in engineering and designing materials and structures that need to minimize friction for efficient functioning.

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