Finding Force Exerted by String on Inclined Planes

[VietDao29]

Hi,
I am writing to ask you guys if it is possible to find the force exerted by the string shown in the following picture.
It may be stupid question,... but please guide me through.
There are 2 boxes lying like that on 2 inclined planes. m1 = 5 kg, m2 = 4 kg. The coefficent of friction is 0.2. I know that the net won't move. So... is there a way to calculate the T (force exerted be the string).
Thanks in advance,
Bye bye,
Viet Dao,

 

[Ameen Khan Gauzel]

Where is the diagram?

 

[dextercioby]

It's there,it says:"Attachements pending approval".It's just that the mentors (one of them,actually) need to both see and say 'yes' to attachements that people are willing to upload on the server.
I guess neither Halls,nor Doc or Integral saw it.

Daniel.

 

[VietDao29]

Hi,
Okay, I don't know why when I sign-in, I can open my image... But when I sign-off, I can't.
Anyway, it's somewhat like this:
- A box number 1 (m1 = 5kg), is lying on an inclined plane (angle: alpha = 30 degrees).
- A box number 2 (m2 = 4kg), is lying on an inclined plane (angle: theta = 60 degrees).
- The 2 inclined planes touch each other at the top (90 degrees). There is a pulley at where the two inclined planes meet each other, and there is a string connects the two boxes.
- Giving that the string and the pulley is weightless.
And find the tension of the string?
Thanks a lot,
Viet Dao,

 

[Doc Al]

Newton's 2nd law

There are 2 boxes lying like that on 2 inclined planes. m1 = 5 kg, m2 = 4 kg. The coefficent of friction is 0.2. I know that the net won't move. So... is there a way to calculate the T (force exerted be the string).

What makes you think that they won't move? Figure it out!

Start by identifying the forces acting on each mass: Tension from the string, weight, and friction. Now write Newton's 2nd law for each mass to get two equations and two unknowns (T and a).

Hint: Since the masses are attached to each other, they will have the same magnitude of acceleration. Also realize that if one mass goes up, the other must go down. So use a sign convention that reflects these facts. To choose a sign convention, arbitrarily guess which way it will move and call that direction the positive direction. Write both equations using the same sign convention.

 

[VietDao29]

Hi,
I really don't think it will move at all. If it moves, then:
$$|P_{1} \sin{\alpha} - P_{2} \sin{\theta}| > F_{sliding friction1} + F_{sliding friction2}$$
If g = 10 m / s^2
Then I will have:
9.641 > 12.66 (that's wrong!)
So... I conclude that the NET won't move.
Am I right?
Viet Dao,

 

[Doc Al]

I really don't think it will move at all. ...
Am I right?

Yes, you are correct. (I need to pay closer attention! )

To find the tension in the string, realize that there is a range of string tensions that will keep each mass from moving. Figure out the range for each mass, and where the ranges overlap. The tension in the string will be in the overlap range. (If the boxes are set up gently, then I would think the tension would be the minimum possible.)

 

[VietDao29]

Hi,
So what you mean is to try to figure out the range of tension in the string for each mass... Yep, it's easy. I can do it.
And what should I do next? I will have two ranges. How can I know the answer?
Is the answer a number or a range, too?
Please help,
Thanks,
Viet Dao,