Simple Experiments with Friction

Now I get to do something with that force scale I built.

I had a request some time ago to talk about friction. Friction is surprisingly complicated. When two surfaces rub against each other, why is there a friction force? The basic answer is that the stuff the two surfaces are made of (atoms) are interacting with each other. If you like, you could think of the bumps on one surface hitting the bumps on the other surface. I know I said it was complicated and that doesn't seem to complicated - does it? The complication comes when you try to model this interaction by looking at either all these bumps or by looking at all the atom-to-atom interactions in the two materials. That would be gianormous number of interactions to consider for a macro-scale object.

If you are ok with a different approach to friction, you can model it quite simply with these two expressions.

Notice that these are not vector equations. Instead, it is a relationship between the magnitude of the frictional force and the normal force (N). The normal force is the force exerted between the two surfaces (which doesn't have to be the weight - just a warning). As for directions, the frictional force is parallel to the surface of the two objects interacting.

The coefficient (mu) is just a parameter that is experimentally determined and depends on the two materials interacting. Notice that there is a different coefficient for static and kinetic (sliding) friction.

On to the first experiment (using the DIY force scale). Here I have a block on a table. I am going to pull on it horizontally with my force scale. Watch what happens.

If you look at the video slowly, you can see that as I pull the force I pull with increases. Remember, the markings on the DIY Force scale are in force units of Lego weights where the first mark is 6 duplo pieces and the second mark is 9 pieces (I will call this unit the LDU - for Lego Duplo Unit). So, if I pull on the block with 8 LDU the block does not move. What is the frictional force in this case? If I pull with 9 LDU, it still doesn't move. It is not until around 10 LDU that it moves and then the scale drops to a much lower value. Here is a diagram.

In both of these cases, the block does not move (doesn't not accelerate). This means that the net force must be zero. What would happen if the friction force was greater than the force I was pulling? This would mean that the net force would be in the direction of the frictional force and the block would accelerate that way. Indeed it would be odd so pull a block to the right and have it accelerate to the left (for a block at rest). And this is why the static friction model has a less-than-or-equal sign.

What about kinetic friction? The video above is not a very good example because the block is not being pulled at a constant speed. I think you can still see that the frictional force to pull it sliding is less than for it stationary.

Let me look at one more case, and then I will offer things that could be explored. What if I pull on the block at an angle above the horizontal? (I guess you noticed the protractor I taped on top of the block) Here is a force diagram for that case (assume I am pulling at a constant speed).

There are a few important things here.

• The net force in the y-direction (vertical) is zero. Since the force from the pull has a y-component, the normal force from the table does not need to be as large.
• Since the normal force is smaller, the frictional force will be smaller.
• All of the force is not pulling against friction, just the x-component of the pulling force.
• Do I need to say it? The total force in the x-direction is zero if it is being pulled at a constant speed.

Let me write the force equilibrium equations for the x- and y-directions:

I guess I never said it, but theta is the angle the force is pulling measured from the horizontal. If I use the model for friction, I can eliminate F_f. I get:

This could be used to solve for the coefficient of friction if you pull at that angle. But maybe that would be boring. Perhaps a better thing to do would be to pull the block at different angles and plot F_p vs.theta. Compare the experimental and theoretical data.

More Stuff to do

Here are some other questions that would be great to look at in a lab. For these, you will be comparing experimental values (say coefficients for different areas). To do this, it will be best to report the uncertainties. Here is an example of uncertainty. Did I not write a basics post on uncertainty? I thought I did.

• Does the coefficient of friction (both kinetic and static) depend on the surface area? Obviously, this model says "no", but does that agree with your data? Collect some experimental data to measure the coefficents for an object and then change the surface area. Can you find some materials that do NOT agree with this model? (hint - you can probably).
• Does the coefficient depend on the mass of the object? Again, the model says it doesn't - still a good thing to look at.
• Does the coefficient depend on speed (for kinetic friction obviously).