How do I calculate the coefficient of friction in a static friction problem?

[Pysics86]

Hi all,
I have problem to solve this question:

Wb=150N
Wa=50N
T=150N
alph =?
µ =?
- There is friction between A and B only(Between A and the ramp there isn't).
- A and B not moving(first Newton's law).

3. I tried to solve as:

But the answer is wrong, can anyone help me please, and explain where is the problem?

Regards Jack.

 

[ehild]

Hi all,
I have problem to solve this question:

Wb=150N
Wa=50N
T=150N
alph =?
µ =?
- There is friction between A and B only(Between A and the ramp there isn't).
- A and B not moving(first Newton's law).

3. I tried to solve as:

But the answer is wrong, can anyone help me please, and explain where is the problem?

Regards Jack.

What is your answer?

 

[Pysics86]

What is your answer?

The correct anser is Miu=0.25
My answer is 0.43.

 

[ehild]

The correct anser is Miu=0.25
My answer is 0.43.

How did you get it?

 

[Pysics86]

By writing the forces as i the diagram forces, did the diagram, i don't care about the final answer and don't care about solving and finding the Miu, what i want to know is if the forces are right as the diagram or not, if not what is the problem, in other world i want to understand the physics not from the question from who understand physics and can explain.

 

[TomHart]

Hi Physics86. Welcome to Physics forums. It looks like your diagrams are correct. The N? in diagram for A would be equal to Nb because those forces have to be equal and opposite. I worked through the problem and got μ = 0.25.

 

[ehild]

By writing the forces as i the diagram forces, did the diagram, i don't care about the final answer and don't care about solving and finding the Miu, what i want to know is if the forces are right as the diagram or not, if not what is the problem, in other world i want to understand the physics not from the question from who understand physics and can explain.

You need to collect the forces acting on block A. You have some confusion here, as there is normal force from the ramp (Na) and there is normal force from B acting on A, that can be the blue vector N?.
The forces acting on B are correct, taking in mind that the normal force Nb is the force exerted by A, and according to Newton's Third Law, it is equal in magnitude to N?.
You need to use the correct magnitudes to get the angle alpha. Remember, the friction is static, so F≤μN, and N is the magnitude of the normal force between A and B.

 

[TomHart]

Remember, the friction is static, so F≤μN

F≤μN. That is an important point. I should have pointed out that, although it wasn't stated, I assumed that one of the conditions of the problem was that block A was just at the point where it was going to slip. In that case, F would be equal to μN (F=μN). Otherwise - if that was not a condition of the problem - you would not be able to calculate μ.