Friction with two blocks and tension

In summary: I feel a lot better now.In summary, the blocks won't move because the static friction is greater than the kinetic friction.
  • #1
fogvajarash
127
0

Homework Statement


A 2.00kg aluminium block and a 6.00kg copper block are connected by a light string over a frictionless pulley. They sit on a steel surface, which is fixed, as shown in the figure, with a (let it be alpha lol) = 43.0deg. The coefficient of static friction for aluminum on steel is 0.56, and for copper on steel is 0.83. Determine whether the blocks start to move once any holding mechanism is released. Then, calculate the sum of the magnitudes of the forces of friction acting on the blocks.

Homework Equations


F = ma

The Attempt at a Solution


The blocks should not move at all according to this equation I've derived (i'm not sure if i should use static or kinetic friction for this case).

a = (m1gsin(a)-us1m1gcos(a)-us2m2g)/(m1+m2)

Where us1 is the coefficient of static friction of copper, m1 is the mass of copper and us2 is the coefficient of static friction of aluminum.

This gives us a negative acceleration and thus the system won't move.

I've determined that the forces of friction for each of the two blocks are the following:

fr1 = us1m1gcos(a) = 10.9872N
fr2 = us2m2g = 35.7294N

I'm using the coefficient of static friction as the two blocks don't move (again not too sure on this one). I've added these two frictions and i got that the final result (46.7N) was incorrect. Or should i do vector addition and determine the magnitude? However, i also did the same and got a wrong result (44.4N).

What should i do?

By the way: i have the following FBDs:

For Al, i have the normal force going upwards, the weigh, the friction and the tension. For Cu, i have the tension going up the plane, the friction up the plane, the normal force perpendicular to the surface and the weigh.
 

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  • #2
fogvajarash said:

Homework Statement


A 2.00kg aluminium block and a 6.00kg copper block are connected by a light string over a frictionless pulley. They sit on a steel surface, which is fixed, as shown in the figure, with a (let it be alpha lol) = 43.0deg. The coefficient of static friction for aluminum on steel is 0.56, and for copper on steel is 0.83. Determine whether the blocks start to move once any holding mechanism is released. Then, calculate the sum of the magnitudes of the forces of friction acting on the blocks.

Homework Equations


F = ma


The Attempt at a Solution


The blocks should not move at all according to this equation I've derived (i'm not sure if i should use static or kinetic friction for this case).
Consider what the words "static" and "kinetic" mean in relation to the words "moving" and "not moving". Is "static" the sort of word you normally associate with movement or with non-movement?

a = (m1gsin(a)-us1m1gcos(a)-us2m2g)/(m1+m2)

Where us1 is the coefficient of static friction of copper, m1 is the mass of copper and us2 is the coefficient of static friction of aluminum.
So m1 is copper and m2 is aluminium ... let me tidy that up for you:

$$a=m_{Cu}g\sin\alpha - (\mu_{Cu}m_{Cu}+\mu_{Al}m_{Al})g\cos\alpha$$

This gives us a negative acceleration and thus the system won't move.
- negative acceleration could be an increase in speed the other way from positive - I think you need to say more than that.

What you mean is that the force supplied by gravity is smaller than the maximum that the static friction can provide.

I've determined that the forces of friction for each of the two blocks are the following:

fr1 = us1m1gcos(a) = 10.9872N
fr2 = us2m2g = 35.7294N
Those are the maximum forces that the friction could provide.
However, the actual friction does not need to be so high.
 
  • #3
Simon Bridge said:
$$a=m_{Cu}g\sin\alpha - (\mu_{Cu}m_{Cu}+\mu_{Al}m_{Al})g\cos\alpha$$
I think you meant
$$a(m_{Cu}+m_{Al})=m_{Cu}g\sin\alpha - \mu_{Cu}m_{Cu}g\cos\alpha-\mu_{Al}m_{Al}g$$
 
  • #4
fogvajarash said:
I've determined that the forces of friction for each of the two blocks are the following:

fr1 = us1m1gcos(a) = 10.9872N
fr2 = us2m2g = 35.7294N
I think you've swapped over the two blocks. m2 is the 6kg copper block on the slope.
 
  • #5
haruspex said:
I think you meant
$$a(m_{Cu}+m_{Al})=m_{Cu}g\sin\alpha - \mu_{Cu}m_{Cu}g\cos\alpha-\mu_{Al}m_{Al}g$$
... actually I meant only to transliterate OPs equation quoted in the same post. ;)

Still - I should have picked that up.
 
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  • #6
I'm so sorry for not replying! (midterms are killing me!)

I figured out the problem. I used the static friction of the blocks and then i determined that the acceleration was negative (thus the blocks aren't moving as the treshold friction isn't surpassed). To obtain the final friction force, i just added up the termins in the equation. We have that mCugsinα = T + fr1 (however, remember that T is actually fr2!) So you just add them up and get the final result.

Thank you Simon.
 

What is friction and tension?

Friction is a force that opposes motion between two surfaces that are in contact with each other. Tension is a force that is transmitted through a string, rope, cable, or any other type of elastic material when it is pulled tight by forces acting from opposite ends.

How does friction affect the motion of two blocks?

Friction between two blocks can cause the blocks to move at different rates, depending on the amount of friction present. If the friction is high, the blocks will move slower, and if the friction is low, the blocks will move faster.

What factors affect the amount of friction between two blocks?

The amount of friction between two blocks is affected by the type of surfaces in contact, the force pressing the surfaces together, and the presence of any lubricants or adhesives.

How is tension calculated between two blocks?

Tension can be calculated using Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. In the case of two blocks connected by a string, the tension can be calculated by finding the net force acting on both blocks and dividing it by the total mass of the blocks.

What is the relationship between friction and tension?

Friction and tension are related in that both forces can affect the motion of two blocks. Friction can cause the blocks to move at different speeds, while tension can help to keep the blocks connected and in motion together.

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