# AP Physics Free Response: Friction between two blocks

• be547
In summary: So by dividing by the weight of C, you get μ.In summary, the conversation discusses a system of blocks connected by cords and a pulley. Block A has a downward acceleration and blocks B and C have a horizontal acceleration. The coefficients of kinetic and static friction are used to determine the coefficient of kinetic friction between blocks B and C. By setting up force equations for each block and using Newton's 2nd law, a coefficient of 0.1 is found.
be547

## Homework Statement

Block A of mass 2M hangs from a cord that passes over a pulley and is connected to block B of mass 3M that is free to move on a frictionless horizontal surface. The pulley is a disk with frictionless bearings, having a radius R and moment of inertia 3MR^2. Block C if mass 4M is on top of block B. The surface between blocks B and C is NOT frictionless. Shortly after the system is released from rest, block A moves with a downward acceleration a and the two blocks on the table move relative t each other

vertical tension in rope on right of pulley = 2Mg-2Ma

horizontal tension on rope on left of pulley = 2Mg-5Ma

Q: if a (linear accel) = 2m/s^2 determine the coefficient of kinetic friction between blocks B and C

## Homework Equations

static friction is less than or equal to coefficient of static multiplied by Fnormal

kinetic F = kinetic coefficient multiplied by Fnormal

## The Attempt at a Solution

i played around with a number of things but really have no clue what I am doing.
i wrote down the idea that the horizontal tension which was found to be 2mg-5ma must be more than the maximum static friction. then I isolated blockc (4M) and found the normal force to be 4MG ( i think) but i cannot figure out where the kinetic frictional force is acting since the both blocks are moving. AP exam on monday. its killing me that i can't get this. PLEASE HELP!

Last edited:
The kinetic friction acts between blocks B and C.

Hint: Identify the forces on block B, the pulley, and block A. Write separate force (or torque) equations for each body, using Newton's 2nd law. You'll get three equations, which you can solve together to find the coefficient of friction.

ok. so i must be missing something fundamental. yesterday i finally found an answer of .1 for the coefficient of kinetic f. but now, isolating block b with friction pulling to the left and horizontal tension as a force on the right i am getting some odd answers that cannot fit a coefficient. ie 4, -2/3

what i did yesterday was i used nsl on block b
T.hor-frict.kin= 3Ma
T.hor = 2Mg-5Ma (from nsl for rotation)
so...
2Mg-5Ma-mk4Mg= 3Ma
cross out Ms
2g-5a-3a=mk4g
sub in g=10 and a=2
20-10-6=mk40
divide by 40
mk=0.1

this seems to be a reasonable answer but i don't understand (if it is right) why it worked with the normal force from block c.
is this even correct?

be547 said:
ok. so i must be missing something fundamental. yesterday i finally found an answer of .1 for the coefficient of kinetic f. but now, isolating block b with friction pulling to the left and horizontal tension as a force on the right i am getting some odd answers that cannot fit a coefficient. ie 4, -2/3
If you want to understand what went wrong, post your work for that solution.

what i did yesterday was i used nsl on block b
T.hor-frict.kin= 3Ma
OK. That's for block B.
T.hor = 2Mg-5Ma (from nsl for rotation)
This is the combined equations for block A and the pulley.
so...
2Mg-5Ma-mk4Mg= 3Ma
cross out Ms
2g-5a-3a=mk4g
sub in g=10 and a=2
20-10-6=mk40
divide by 40
mk=0.1
Sounds good.

this seems to be a reasonable answer but i don't understand (if it is right) why it worked with the normal force from block c.
Not sure I understand your question. The friction between C and B equals μN. N is just the weight of block C.

## 1. What is friction and how does it affect the motion of two blocks?

Friction is a force that opposes the relative motion between two surfaces in contact with each other. In the case of two blocks, friction acts to resist the motion of one block relative to the other, causing them to either move together or in opposite directions.

## 2. How do you calculate the coefficient of friction between two blocks?

The coefficient of friction can be calculated by dividing the magnitude of the frictional force by the normal force between the two blocks. This can be determined experimentally by measuring the force required to move one block over the other, and dividing it by the weight of the block.

## 3. How does the mass of the blocks affect the friction between them?

The mass of the blocks does not directly affect the friction between them. However, a heavier block will have a greater normal force acting on it, which in turn will result in a greater frictional force between the two blocks.

## 4. Can friction between two blocks be reduced or eliminated?

Friction between two blocks can be reduced by using a lubricant between the surfaces, or by using materials with lower coefficients of friction. However, it cannot be completely eliminated as there will always be some resistance to motion between two surfaces in contact.

## 5. How does the angle at which the blocks are placed affect the friction between them?

The angle between the two blocks does not directly affect the friction between them. However, if the blocks are placed at an angle on an inclined surface, the normal force between them will change, resulting in a different frictional force. This can be calculated using trigonometric functions.

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