Calculating Coefficient of Kinetic Friction for a Hockey Puck

[Psyguy22]

A hockey puck on a frozen pond with an initial speed of 12.3 m/s stops after sliding a distance of 198.9 m. Calculate the average value of the coefficient of kinetic friction between the puck and the ice.

So I started with finding the acceleration. I divided 12.3m/s by 198.9m then took the inverse (so units would go back seconds) and came up with 16.17s. So now I have Δv and Δt so I divided 12.3m/s by 16.17s to get an acceleration of .76m/s^2

I also know that friction equals μN and that F=ma. Since N=mg and friction is the only force acting on the object, i divided the mass out. So I had μg=a, or μ=a/g. (using 9.81m/s^2 as gravity) So μ=.0774 which seemed reasonable for ice. But I don't know how to find the actual force without knowing the mass. Am I even heading in the right direction?

 

[mfb]

So I started with finding the acceleration. I divided 12.3m/s by 198.9m then took the inverse (so units would go back seconds) and came up with 16.17s. So now I have Δv and Δt so I divided 12.3m/s by 16.17s to get an acceleration of .76m/s^2

That does not work.
To travel 198.9m in 16.17s, it would have to travel at 12.3m/s the whole time, which is clearly not the case. You need a different approach here.

I also know that friction equals μN and that F=ma. Since N=mg and friction is the only force acting on the object, i divided the mass out. So I had μg=a, or μ=a/g. (using 9.81m/s^2 as gravity) So μ=.0774 which seemed reasonable for ice. But I don't know how to find the actual force without knowing the mass. Am I even heading in the right direction?

That part is good, once you fix your acceleration value. You cannot, and do not have to, calculate the force.

 

[Psyguy22]

Then how do I find acceleration? I don't have time..

 

[MalachiK]

But you do know lots of other things. For example, you know the initial and the final speeds. I think it's okay to assume uniform acceleration here. You probably have a list of equations for dealing with this sort of motion that look something like, for example, v = u + at.

What you need to do is find an equation that includes the quantities that you know along with the acceleration. Then there's some algebra to find a.

 

[Nickie]

Yes, you are heading in the right direction. To calculate the coefficient of kinetic friction, you need to first calculate the acceleration of the hockey puck. This can be done by dividing the initial velocity by the distance traveled, as you have correctly done.

Next, you need to find the normal force acting on the puck. This is the force that the ice exerts on the puck, which is equal to the weight of the puck (mg). Since you do not have the mass of the puck, you can use the formula μ = a/g, where μ is the coefficient of kinetic friction, a is the acceleration you calculated, and g is the acceleration due to gravity (9.81 m/s^2).

Therefore, μ = 0.76 m/s^2 / 9.81 m/s^2 = 0.0774. This is the average value of the coefficient of kinetic friction between the puck and the ice.

To find the actual force of friction, you can use the formula F = μN, where F is the force of friction, μ is the coefficient of kinetic friction, and N is the normal force. Since you have already calculated μ, you can now find the force of friction by multiplying it by the normal force (mg).

In conclusion, your calculation of the coefficient of kinetic friction for the hockey puck on the frozen pond seems reasonable and correct. However, to find the actual force of friction, you will need to know the mass of the puck.