Mechanics problem with two masses, a pulley and friction

[Ahmed Ayman]

Can anyone please explain to me how can I calculate the "Tension" and "acceleration" of M in this question interms of M,m1,m2 and g?
I can't understand how M has an acceleration or why M is involved in the calculation of the tension
my solution was that acc of M is zero
and Tension = m1g x (m2/(m2+m1))
Thanks in advance

 

[Chestermiller]

Can anyone please explain to me how can I calculate the "Tension" and "acceleration" of M in this question interms of M,m1,m2 and g?
I can't understand how M has an acceleration or why M is involved in the calculation of the tension
my solution was that acc of M is zero
and Tension = m1g x (m2/(m2+m1))
Thanks in advance

View attachment 233921

What is the tension in the rope (assuming M is not moving)? From a free body diagram of M (including the attached pulley), what are the forces acting on M?

 

[Ahmed Ayman]

What is the tension in the rope (assuming M is not moving)? From a free body diagram of M (including the attached pulley), what are the forces acting on M?

the question didn't mention any external force, it just said that m1 can only move in the vertical direction plus that there is no friction in the whole system

 

[jbriggs444]

the question didn't mention any external force

The question does assume one external force in particular. But leave that to one side. What internal forces act on M?

 

[Ahmed Ayman]

The question does assume one external force in particular. But leave that to one side. What internal forces act on M?

 

[jbriggs444]

[a graphic showing the problem]

The question was addressed to you, not to the textbook. You should be able to draw a set of free body diagrams, one for each object in the system. The question at hand is about the forces that act on M.

 

[Ahmed Ayman]

The question was addressed to you, not to the textbook.

that is the same question I'm trying to solve!

 

[jbriggs444]

that is the same question I'm trying to solve!

Yes, you have quoted the problem from the textbook. Yes, that is the problem that you are trying to solve. But you have been asked a question several times now about an inventory of forces that act on M. We are not asking for a numerical answer. We are just looking for you to identify those forces so that you could portray them in a free body diagram.

The goal is to be able to write equations that relate the various forces and accelerations that you identify. The first step is to identify the forces.

 

[Ahmed Ayman]

Yes, you have quoted the problem from the textbook. Yes, that is the problem that you are trying to solve. But you have been asked a question several times now about an inventory of forces that act on M. We are not asking for a numerical answer. We are just looking for you to identify those forces so that you could portray them in a free body diagram.

The goal is to be able to write equations that relate the various forces and accelerations that you identify. The first step is to identify the forces.

Oh sorry !
actually that is the main problem for me... I thought that M is affected by the weight and the normal force but I can't figure a relation between M and the tension.
sorry for not understanding your reply before!

 

[CWatters]

There are other forces. If M is accelerating to the right what about m1?

What about m2?

 

[jbriggs444]

I thought that M is affected by the weight and the normal force but I can't figure a relation between M and the tension.

It is good that we are no longer talking at cross purposes. Yes, M's own weight and the normal force from the table on which it rests are two things that act on M. There are others. Consider, for instance, block m₂. Does it exert any force on M?

But your primary concern is with tension and how it relates to M. Let us look more closely at that. Consider the pulley. What forces act on the pulley?

 

[Ahmed Ayman]

It is good that we are no longer talking at cross purposes. Yes, M's own weight and the normal force from the table on which it rests are two things that act on M. There are others. Consider, for instance, block m₂. Does it exert any force on M?

But your primary concern is with tension and how it relates to M. Let us look more closely at that. Consider the pulley. What forces act on the pulley?

The tension ?

 

[Ahmed Ayman]

There are other forces. If M is accelerating to the right what about m1?

What about m2?

but how did you know that M is accelerating to the right?

 

[jbriggs444]

The tension ?

That's close. I am going to spoon feed you this part of the answer.

You have the tension from the rope segment leading off to the left. That results in a leftward force on the pulley. You have the tension from the rope segment leading down to m1. That results in a downward force on the pulley. You have the force from the attachment of the pulley to M.

Strictly speaking, "tension" is more a condition in a rope than it is an actual force. Tension results in a force at its point of attachment. That force is equal to the magnitude of the tension. It acts on the attachment point and has a direction pointed from the attachment point along the direction of the rope.

For an ideal pulley, the tension on the rope segment coming off on the one side is equal to the tension in the rope going in the other. However, those directions are almost always different, so pulleys are almost always under a net force due to the tension. You can treat a pulley as if the rope is "attached" to the pulley wheel at two points, one where it goes in and the other where it comes out.

 

[Ahmed Ayman]

That's close. I am going to spoon feed you this part of the answer.

You have the tension from the rope segment leading off to the left. That results in a leftward force on the pulley. You have the tension from the rope segment leading down to m1. That results in a downward force on the pulley. You have the force from the attachment of the pulley to M.

Strictly speaking, "tension" is more a condition in a rope than it is an actual force. Tension results in a force at its point of attachment. That force is equal to the magnitude of the tension. It acts on the attachment point and has a direction pointed from the attachment point along the direction of the rope.

For an ideal pulley, the tension on the rope segment coming off in the one side is equal to the tension in the rope going out the other. However, those directions are almost always different, so pulleys are almost always under a net force due to the tension. You can treat a pulley as if the rope is "attached" to the pulley wheel at two points, one where it goes in and the other where it comes out.

then the other force acting on M = the resultant of the two forces acting on the pulley ?

 

[jbriggs444]

then the other force acting on M = the resultant of the two forces acting on the pulley ?

Yes.

 

[Ahmed Ayman]

Yes.

Ok thank you so much and sorry for wasting your time !

 

[Chestermiller]

The reason you are having so much trouble with this problem is that you have not drawn a free body diagram for the combination of M together with its attached pulley. Do you really feel that you have advanced to the point where you no longer need to use free body diagrams?

 

[Ahmed Ayman]

The reason you are having so much trouble with this problem is that you have not drawn a free body diagram for the combination of M together with its attached pulley. Do you really feel that you have advanced to the point where you no longer need to use free body diagrams?

lol, I am really sorry, I thought I was able to imagine it but I will never forget to draw free body diagram again.. thank you for your help

 

[CWatters]

but how did you know that M is accelerating to the right?

There appears to be an outside force F acting on it to the right and no friction.

 

[jbriggs444]

There appears to be an outside force F acting on it to the right and no friction.

However, the full text in #5 reads "Let the force $\vec{F}$ be zero".

 

[vela]

lol, I am really sorry. I thought I was able to imagine it but I will never forget to draw free body diagram again.. thank you for your help

It's good that you recognize the error of your ways!

I'm betting that your instructor has advised you to draw a free-body diagram, your textbook says to draw a free-body diagram, and people in this thread suggested you draw a free-body diagram, yet you still neglected to follow this advice. Spend some time being metacognitive and ask yourself why you ignored all this advice and how you can avoid making similar mistakes in the future. It will help you become a better learner.

 

[Ahmed Ayman]

Ok,Thank you so much

 

[CWatters]

However, the full text in #5 reads "Let the force $\vec{F}$ be zero".

Sorry I missed that.