How Do I Calculate Kinetic Friction Using Work and Force Data?

[Cbeppe]

Homework Statement

The task was to find the kinetic friction of a puck that is shot from an elastic string. The puck was sliding on a cardboard plane. To do this, I was advised find the work done on the puck, and have therefore collected the following data:

• Distance Traveled
• Force the string in Newtons (Found by conecting a Newton meter to the string and pulling)
• Work Done in Joules
• Weight of the puck
• I was also advised to find the angle of the plane at which the puck started sliding.

Homework Equations

E_p=1/2kx²

The Attempt at a Solution

First, I had to find the potential energy stored in the spring by using the formula:
E = ½kx² where x is equal to the distance traveled by the puck. I found the spring constant through this equation:
k = ma/x where m is the mass, and a is the acceleration. This can be simplified to k=F/x, where F is force because F=ma. With this formula, I found k by using the force of the string as described above. X was explained to me as the distance traveled by the puck, and is therefore a part of my collected data.

Through these steps, I found the potential elastic energy in the system.
However, I do not know what to do from here. How do I use the information I have gathered to determine the friction excerted on the puck?

I'm very reluctant to ask for a full solution, since I want to learn this. I have spent the best part of the evening twisting my brains about this, and posting here is only a last resort. If anyone could give me a nudge in the right direction, it would be very appreciated.

This is my first time posting here, so if I missed anything, or you need more details, please ask.

Thanks a lot.

 

[G01]

At first glance I see one misconception in your work.

In the formula:

$$E=\frac{1}{2}kx^2$$

x is not the distance traveled by the puck. It is the distance the spring was compressed.

This should make some sense right? That formula is measuring the energy stored in the spring. Therefore the quantities involved should relate to the spring in some way.

 

[Delphi51]

Welcome to PF, cbeppe.
At first look, it seems to me you could assume all the spring energy E is passed on to the puck. It loses energy due to friction as it travels. The big picture is: E = work done against friction.
Fill in the details and solve that for the kinetic coefficient of friction.

What was that about an angle? Do you mean the string pulled the puck at an angle with the cardboard plane? If so, you'll have to consider only the horizontal component of the force doing work on the puck. The force diminishes as the stretch length diminishes, so it will get quite complicated. Even the normal force will vary as the string pulls the puck upward! Do you know calculus?

 

[Cbeppe]

First of all, thanks for taking the time, both of you.

@G01:
Yes, that makes a lot more sense... can't believe I didn't notice that.

@Delphi
Sorry, that was a bad explanation about the angles. It works like this.

The puck is put on a plane and one edge of the plane is raised so as to increase it's angle towards the ground. I was supposed to record the angle at which the puck started sliding, and this should then help me find the friction.

Unfortunately, my physics class and my math class is not aligned. Some of the physics could be easier with calculus, but I have never learned it in a math class. However, I think with this clarification on how the inclined plane works, the calculus might not be necessary.

Again, thanks for looking into my problem :)

 

[Delphi51]

Yikes, I didn't notice the x misunderstanding either.
The angle measurement will enable you to find the coefficient of static friction but is no help on the kinetic friction problem.

Most of us have experienced the calculus/physics misalignment. It turns out not to be much of a problem.

 

[Cbeppe]

¨I guess I'll leave the incline out of it then.

With your help, I have come up with this for one of the measuremnts we took:

String Extention (x) = 0.4m
Distance Traveled by puck (s) = 0,205m
Force on String (F) = 1N

W = F*s
W = 0,205 J

E = (1/2)k*x^2
E = (1/2)(F/x)x^2
E = (1/2)(1/0.4)16
E = 20

So from that, I have a value for energy, and a value for work done. However, I'm not sure how to go from here. Since work is the change in energy, it would make sense to say that friction = E-W or 19.795, because E1-E2=0.205. However, this doesn't seem quite right for me.

Do you see where I am going wrong?

Thanks once again

 

[Delphi51]

I would first of all figure out the constant k once and for all:
Assuming the force of 1 N caused the string to stretch 0.4 m,
F = kx, k = F/x = 1/0.4 = 2.5

Then E = ½kx² = ½*2.5*0.4² = 0.2 Joules.
Oh, oh. This seems too small. Not enough energy to shoot a puck.
Have I misunderstood your numbers?

The next step would be to say
Energy of spring = work done against friction
0.2 = Ff*d
0.2 = μ*Fn*d
and solve for the coefficient of kinetic friction, μ.
Here d is the distance the puck traveled, Fn the weight of the puck.

 

[Cbeppe]

Thanks a lot Delphi, that's just what I needed. It seems I didn't change one of my x's to SI Units in the post above. Anyway, that last formula got me right on track. Thanks a bunch.

The numbers are a little weird, but it's all I've got. The "puck" isn't the ice-hokey type, it only weighs 27 grams, but it still seems a little low.