The first mass weighs 2 lbs., not 1.5 lbs. You got most of it correct, but you missed in a couple of places with this error. If you make the necessary corrections, I think you will find the results useful in understanding the concept of coefficient of friction. ## \\ ## One additional problem for you: Increase the mass to weigh ## F_N= 5## lbs. Compute the expected force required to pull it across the rough surface. Also, compute the force you would likely need to pull it across the surface of ice.

Then this is the crux of your problem. To show that μ does not depend on the weight \ mass is an experimental question (at this level *) so you do need to measure the forces. Any argument that starts with F_{f} = μ * F_{n} is going to be circular, because it assumes μ does not vary with mass.

So if you don't have the tools you need, you have to use the tools you have or can make. For example, you can make your own force meter with a spring or elastic band and a ruler or produce forces by hanging weights and transmit the force with string.

You don't need to work in any particular units - you can define your own. So if you pull the book across the table by hanging a bag of marbles on a piece of string over the edge of the table, you can measure F_{f} in "marbles force". These won't be very precise tools, but doing this sort of expt should really help you.

And the mass of the book could be varied by having several similar books and piling them on top of each other. Then you measure mass in "books" and F_{n} in "books force" and end up with μ in marbles force per book force or marbles per book. That's fine. If it takes the same number of marbles per book for different size piles, you'll have proved the point.

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You do raise the very interesting question about how close the results need to be. I think your results will be very rough.
If the results vary at random on different trials, you might say, 'ok, μ may be constant but there are a lot of random errors from my bad expt.'
If the results vary consistently - say μ is always bigger when mass is bigger - then even if the numbers are close, you might suspect that μ is not constant.

IMO it is up to you and how much you want to believe in the laws of friction ! But get some results first and we can talk about that.
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(* You can deduce μ from a model, which predicts it will be approximately constant over a range of F_{n} for flat, dry surfaces. But I'm sure that's not what is wanted here.)