Finding mass within a pulley system. Finding coefficient of friction

Serendipitydo

Ok so I'm in college upgrading, and doing my physics 20. I have a hand in assignment due Wednesday and I can't for the life of me figure out these two questions.

6. The 4.0kg block shown accelerates across a frictionless horizontal table at 1.5m/s².
Find the mass of object m1

A. 0.61kg B. 0.72kg C. 6.0kg D. 26kg

For m1 I have: F_N=Fg. Fg=mg, so 39N. F_T-0(no Ff)=ma . So F_T is 6.0N. And then I'm lost.


8. A 45kg toboggan and rider decelerate on level show at 0.53m/s². What is the coefficient of friction between the toboggan and the snow?

A. 0.012 B. 0.054 C. 0.22 D. 0.53

I got that F_N=Fg. Fg=mg so 441.45N(rounded to 2SD). F_net=ma so 24N. And then I'm lost. I know that μ=Ff/F_N

Someone help me please!

NascentOxygen

You have a combined mass of M1 + M2 being accelerated (together). Write an equation for the force that is needed to accelerate such a mass.

Serendipitydo

I got the mass...I think. F_T=ma. 6.0N=m₁(9.81m/s²) So m₁=0.6112kg

Now for the other one...

Serendipitydo

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Ok I think I solved it. Ff is Fnet in the direction of acceleration? So since it's decelerating, wouldn't it accelerate in the direction of the friction?

So Ff=ma
Ff=24N

μ=Ff/FN
μ=24N/441N
μ=0.05442

NascentOxygen

Not so fast. You haven't got this one right, yet. You must determine the force needed to accelerate the combined masses, since they accelerate together.

Serendipitydo

But I only need the mass of the one.

SammyS

NascentOxygen has asked you this question for a reason. Answering it will help you answer the question asked in the problem. More importantly, it should help you understand how to approach such a problem in general.

Serendipitydo

I'm not having problems with the others, just when I need to find a mass with minimal info.
Fg1-FT=ma
Use the total mass of the system. The difference of force of gravity and tension on the rope would be the net force acting on the system.

NascentOxygen

The question supplies all the information you need. You have a mass (M1 + M2) being accelerated. The force that is causing the acceleration is the weight of M1.

One equation, one unknown.

NascentOxygen

That looks right.

Serendipitydo

Thanks for your help. I tend to overthink these things