# Finding the coefficient of kinetic friction of 3 blocks

## Homework Statement

When three blocks are released from rest, they accelerate with a magnitude of 0.500 m/s2. Block 1 has mass M, block 2 has 2M, and block 3 has 2M. What is the coefficient of kinetic friction between block 2 and the table?
(The blocks are arranged with block 1 hanging from the left side of the table, block 2 sitting on the middle of the table, and block 3 hanging from the right side of the table. All connected by an ideal rope.)

fk=ukFN
F=ma

## The Attempt at a Solution

This is the problem. I have no clue where to start. The only thing I know is that the coefficient of friction is uk and has no units. I understand that I must use the first formula somehow. Would I first find the normal force of block 2? I'm lost...

PeterO
Homework Helper

## Homework Statement

When three blocks are released from rest, they accelerate with a magnitude of 0.500 m/s2. Block 1 has mass M, block 2 has 2M, and block 3 has 2M. What is the coefficient of kinetic friction between block 2 and the table?
(The blocks are arranged with block 1 hanging from the left side of the table, block 2 sitting on the middle of the table, and block 3 hanging from the right side of the table. All connected by an ideal rope.)

fk=ukFN
F=ma

## The Attempt at a Solution

This is the problem. I have no clue where to start. The only thing I know is that the coefficient of friction is uk and has no units. I understand that I must use the first formula somehow. Would I first find the normal force of block 2? I'm lost...

## The Attempt at a Solution

Think globally.

The total system has mass 6M

A force equal to the weight of 2M is trying to pull it one way, while a force equal to the weight of 3M tries to pull it the other way.

That means a net force equal to the weight of 1M is accelerating the masses in a given direction.

The "weight of 1M" acting on a total of 6M should give an acceleration you can calculate.

However, due to friction between the 1M block and the table, the acceleration is reduced to only 0.5. from that you can calculate the size of the firction force, and thus the coefficient of friction.

Wouldn't the total mass be 5M? The block hanging from the left side of the table is M, middle block is 2M, and the block hanging from the right side is also 2M. I guess it would still mean that a mass of 1M is accelerating the masses though. I don't understand why I would have to calculate the acceleration when it is given as .500 m/s2 in the problem. Would I use F=ma?

PeterO
Homework Helper
Wouldn't the total mass be 5M? The block hanging from the left side of the table is M, middle block is 2M, and the block hanging from the right side is also 2M. I guess it would still mean that a mass of 1M is accelerating the masses though. I don't understand why I would have to calculate the acceleration when it is given as .500 m/s2 in the problem. Would I use F=ma?

You're right. Total 5M. Mis-read and with no diagram.

If you calculate what the acceleration "would have been" in the absence of friction, you can easily assess the effect of friction - how strong it is.

You can calculate via forces, but I find it easier to work through acceleration.

eg with g=10

Net force equivalent to on 1M, but system mass 5M thus acceleration only 1/5 th of normal [without friction] so 2 m/s2.

Actual acceleration only 0.5, so 3/4 of the net force above is "cancelled by friction" Thus Friction is 3/4 the weight force of M - which is 3/8 or 2M (the Normal Reaction Force for the mass on the table).

Now when you use g = 9.8 or 9.81 you get decimals all over the place, but the idea is the same.

What a pity the standard metre wasn't just a little bit shorter, so that g actually equalled 10.