Rope Tension in Static Equilibrium

In summary, a 25kg weight is suspended from a rope attached to one wall and wrapped around a pulley attached to another wall. The angles at which the ropes meet the walls are provided and the goal is to find the force of tension in each rope. Using the equations EFx=0 and EFy=0, the force of tension in rope A is calculated to be 246N and the tension in rope B is 172N. This solution is confirmed by the fact that the tension in rope A is equal to the force of gravity acting on the weight.
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Homework Statement


A hanging weight with a mass of 25kg is suspended from a rope from a wall. The rope with the weight is wrapped around a pully which is also attached to a different wall. The angle that rope a(rope with mass) makes with the wall is 41 degrees, and the angle of the other rope with the other wall is 69.5 degrees. Find the force of tension in each rope.
326474009_213d9b4c35_o.jpg



Homework Equations


EFx=0
Efy=o


The Attempt at a Solution


EFx=0
Acos(49)-Bcos(20.5)=0
A=Bcos(20.5)/cos(49)
EFy=0
Asin(49)+Bsin(20.5)=mg
(Bcos(20.5)/cos(49))sin(49)+Bsin(20.5)=mg
B=172N
Substitute B back into A
A=172cos(20.5)/cos(49)
A=246

I got the force of tension in A to be 246N and the tension in B to be 172N. Is this correct or am I making this to easy? Also is it just a conicedence that the tension on the rope with the weight is the force of gravity?
Thanks for your help.
 
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  • #2
Looks good to me, although next time, please provide equations and values you have calculated. It's a lot easier to check your calculations than do them ourselves!
 
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  • #3
Oh, now youve added the picture.. it's not what I thought! I'd imagined both ropes attached to the mass, and the pulley on the left hand wall (for some reason!) Should still be right though.. just draw a free body diagram at the point at which rope A meets rope B and set up the equations from there.
 

1. What is rope tension in static equilibrium?

Rope tension in static equilibrium refers to the force exerted on a rope or cable when it is not moving and is in a state of balance or stability.

2. How is rope tension calculated?

Rope tension can be calculated by using the formula T = W + F, where T is the tension force, W is the weight of the object being supported by the rope, and F is the external force acting on the rope.

3. What factors affect rope tension?

The factors that affect rope tension include the weight of the object being supported, the angle at which the rope is pulled, and any external forces acting on the rope.

4. How is rope tension used in real-life applications?

Rope tension is used in various real-life applications such as construction, rock climbing, and sailing. It is also important in engineering and physics for understanding the stability and strength of structures.

5. What happens if rope tension is not in static equilibrium?

If rope tension is not in static equilibrium, the rope will either break or the object being supported will fall. This is because the forces acting on the rope are not balanced and there is a net force causing movement.

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