Mass of a weight attached to a body

[AndrejN96]

Homework Statement

A weight is attached to a wooden body with mass M=4kg lying on a horizontal surface. The coefficient of friction is μ=0.2. What is the mass m of the weight so that the wooden body is moving?

Image:

Homework Equations

Equations of forces

The Attempt at a Solution

I tried drawing all the forces that apply on both bodies and then make an inequality where the total sum of the forces applying on the weight is bigger than the ones on the wooden body, but I get an unknown value for the acceleration. Help would be appreciated.

 

[Chestermiller]

Hi AndrejN96. Welcome to Physics Forums.

The problem statement isn't clear. Is this the exact wording? If not, please provide the exact wording.

Chet

 

[mfb]

I tried drawing all the forces that apply on both bodies and then make an inequality where the total sum of the forces applying on the weight is bigger than the ones on the wooden body, but I get an unknown value for the acceleration. Help would be appreciated.

The approach looks good. To see what went wrong, please show your full work here.

 

[AndrejN96]

Hi AndrejN96. Welcome to Physics Forums.

The problem statement isn't clear. Is this the exact wording? If not, please provide the exact wording.

Chet

Hi, yes this is the exact wording, as taken from a college exam, just translated to English.

The approach looks good. To see what went wrong, please show your full work here.

This is what I'm currently at: http://i.imgur.com/TDftcan.png

I've gathered the sums of the forces by x and y-axis of the two objects as presented to us in class and now I am unsure how to continue.

 

[Chestermiller]

I'm going to make some guesses about this problem statement, which has probably lost some things in the translation.

1. The coefficient of friction that is given is the coefficient of static friction
2. The question should read: What is the mass m of the weight so that the wooden body just begins to move?

So I think we are dealing with a static friction problem here, and the system is in static equilibrium, but on the verge of moving.

Chet

 

[AndrejN96]

I'm going to make some guesses about this problem statement, which has probably lost some things in the translation.

1. The coefficient of friction that is given is the coefficient of static friction
2. The question should read: What is the mass m of the weight so that the wooden body just begins to move?

So I think we are dealing with a static friction problem here, and the system is in static equilibrium, but on the verge of moving.

Chet

You're probably correct. I am unsure as what the terminology is in English as translating it literally from my language just makes no sense. I did manage to solve it myself though, solving for acceleration and then finding values for m so that a>0.

 

[Satvik Pandey]

The problem asks us to find the 'm' at which wooden block begins to move. In such types of problem the acceleration of the system tends to be zero.
So you equations should be
##f_{t}=T##
and ##T=mg##
Can you find ##m## from here?

 

[AndrejN96]

The problem asks us to find the 'm' at which wooden block begins to move. In such types of problem the acceleration of the system tends to be zero.
So you equations should be
##f_{t}=T##
and ##T=mg##
Can you find ##m## from here?

Oh, so the acceleration should be zero at that point?

 

[mfb]

Just before the block begins to slide (but is still not moving), the acceleration is zero, yes.