# Min. and max. mass to keep pulley system stationary

1. Dec 26, 2015

### Alexstrasza

1. The problem statement, all variables and given/known data
The pulley system is stationary. What is the maximum and minimum mass of block B to keep the system stationary?

We know that:

Mass of A = 100 kg
Angle = 45 degrees
μ = 0.1

2. Relevant equations
F = ma

3. The attempt at a solution
I know that in order for the system to stay stationary the forces in both directions must be equal. I also know that the maximum mass of B is when the system almost slides to the left, and minimum is when it almost slides to the right.

I'm not sure how to use the equation for minimum or maximum.

I thought the equation for moving to the left direction would be:

(mass of B)(gravity) - T = T - sin(45)(mass of A)(gravity) - Force of friction

But then how would we find T? And is this the right equation for the maximum?

2. Dec 26, 2015

### BvU

Hello Alexstrasza,

Do you know how to calculate the maximum friction force from the given information ?
And which way can it work ?

3. Dec 26, 2015

### Alexstrasza

Thank you. :)

I tried to find the force of friction = μ * (F normal) = 0.1 * (cos(45)mg) = 70.7 N

But I don't know how to find maximum or minimum friction force. What is the range? Given that the coefficient of friction is 0.1 I would assume that is the maximum but what is the minimum? 0?

4. Dec 26, 2015

### haruspex

The two blocks do not "know" about each other. Each moves or stays put according to the forces acting directly on it. This gives two equations, not one.

5. Dec 26, 2015

### Alexstrasza

Thank you!

I wrote new equations and I think I solved it.

1) For maximum mass, the direction of block B pulling down is positive, so:

(mass of B)(g) = T
T = sin(45)(mass pf A)(g) + friction force = 707.1 + 70.7

(mass of B)(g) = 777.8
mass of B = 77.78 kg (our teacher allows us to use 10 m/s^2 for gravity instead of 9.8)

2) For minimum mass, the direction is flipped and so is the friction force, so I got:

sin(45)(mass of A)(g) - friction force = T
T = (mass of B)(g)

(mass of B)(g) = 636.4
mass of B = 63.64 kg

Please let me know if this is correct.

6. Dec 26, 2015

### BvU

Excellent ! Well done .

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