# Friction in a 3 block and pulley system

• Maximusw47
In summary, the block of mass 3 will move if the coefficient of static friction between blocks 1 and 2 is greater than the coefficient of kinetic friction between block 2 and the horizontal surface.
Maximusw47

## Homework Statement

A block of mass m1 is on top of a block of mass m2. Block 2 is connected by an ideal rope passing through a pulley to a block of unknown mass m3 as shown. The pulley is massless and frictionless. There is friction between block 1 and 2 and between the horizontal surface and block 2. Assume that the coefficient of kinetic friction between block 2 and the surface, μ, is equal to the coefficient of static friction between blocks 1 and 2.
What is the minimum value of m3 for which block 1 will start to move relative to block 2?

F=ma
f= mu*N

## The Attempt at a Solution

I've taken a couple of approaches. The one I think is most valid is this: The point just before block 2 slips relative to block 1 is where the static friction between m1 and m2 reaches its maximum value. At this point the magnitude of acceleration between all the blocks is the same. I'm then solving for:

m1*a = mu*m1*g
m2*a = T-mu*m1*g-mu*(m1+m2)*g
m3*a=T-m3*g

Which gives me:
m3=2*mu*(m1+m2)/(1+mu)

Which is wrong. Am I making a math error or taking the wrong approach entirely?

Thanks in advance for any help!

Can you post the diagram or facsimile thereof?

Maximusw47 said:
m1*a = mu*m1*g
m2*a = T-mu*m1*g-mu*(m1+m2)*g
m3*a=T-m3*g
You have it almost right, except your sign-convention is inconsistent:
"a" is supposed to be the same for all three equations, right?
In the first two equations, "a" takes a positive value, but in the third equation "a" takes a negative value (m3g ≥ T)

Nathanael said:
You have it almost right, except your sign-convention is inconsistent:
"a" is supposed to be the same for all three equations, right?
In the first two equations, "a" takes a positive value, but in the third equation "a" takes a negative value (m3g ≥ T)
Got it. Thanks.

## 1. What is friction in a 3 block and pulley system?

Friction refers to the resistance force that occurs when two surfaces come into contact and move against each other. In a 3 block and pulley system, friction can occur between the blocks and the surface they are resting on, as well as between the pulley and the rope or belt.

## 2. How does friction affect the movement of the blocks in a 3 block and pulley system?

Friction can cause a decrease in the speed and efficiency of the blocks' movement in a 3 block and pulley system. This is because the force of friction acts in the opposite direction of the movement, creating resistance and reducing the overall motion.

## 3. Can friction be reduced in a 3 block and pulley system?

Yes, friction can be reduced in a 3 block and pulley system by using lubricants between the surfaces, choosing smoother materials for the blocks and pulley, and minimizing the weight and pressure on the system.

## 4. How does the angle of the rope or belt affect friction in a 3 block and pulley system?

The angle of the rope or belt can increase or decrease the amount of friction in a 3 block and pulley system. A smaller angle can reduce the force of friction, while a larger angle can increase it.

## 5. What are some real-life examples of friction in a 3 block and pulley system?

Friction in a 3 block and pulley system can be observed in various mechanical systems such as elevators, cranes, and conveyor belts. The resistance created by friction helps to control and regulate the movement of heavy objects in these systems.

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