Solving Pulleys and Forces Homework Problem

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Homework Statement

An object of mass 12.5 kg hangs from very light pulleys as shown here:
http://i26.tinypic.com/24lq5b4.jpg
What force must be applied to the rope so that the mass stays at rest?

Homework Equations

Fnet = ma...

The Attempt at a Solution

I am really clueless when it comes to this question. I know the net force must be 0 because there is no acceleration occurring b/c it must be at rest. Please help.

 

[magda3227]

You are correct by saying that the net force must be 0, since the system will be in static equilibrium.
Try drawing a free body diagram for each pulley.
If you correctly label the tensions in the strings and sum up the forces in both the x and y directions, the problem will become much easier.

 

[Moetasim]

Hello,

Thank you for sharing your question. I would approach this problem by first identifying the forces acting on the object. In this case, there are two forces: the force of gravity pulling the object downward with a magnitude of 12.5 kg * 9.8 m/s^2 (assuming standard gravity), and the tension force from the rope pulling the object upward.

Since the object is at rest, we know that the net force must be zero. This means that the tension force must be equal in magnitude to the force of gravity, but in the opposite direction. This is because the two forces are balancing each other out, resulting in a net force of zero.

Using the equation Fnet = ma, we can rearrange it to solve for the tension force, which is the force we are looking for. So, the equation becomes Fnet = m * 0, which simplifies to Fnet = 0. This shows us that the tension force must be equal to the force of gravity, which is 12.5 kg * 9.8 m/s^2, or approximately 122.5 N.

I hope this helps in solving the problem. Let me know if you have any further questions. Good luck with your homework!

Best,