# Finding Tension in a Pulley System

• Becca93
In summary, the question asks for the minimum tension needed to slowly raise a crate using frictionless pulleys. After multiple attempts, the correct calculation for the full tension was found to be 47.4 N, which was obtained by taking the force down as the sum of the masses and using trigonometry to find the tension in the cable.

#### Becca93

Homework Statement

A crate is pulled up using frictionless pulleys in the manner shown in the figure. The angle is 45 degrees. The masses are, for the small pulley, m1=4.1 kg, for the traveling pulley, M2=6.7 kg, and for the crate, MC=45.8 kg. What is the minimum tension with which the operator must pull on the cable (assume the cable is of neglible mass) in order to slowly raise the crate.
(The diagram of this is attached.)

The attempt at a solution

I've tried this a few times now and have yet to get the right answer. First, I took the Mc and M2 as the force down, which meant the tension in each of the cables it was attached to was g(1/2)(M2+Mc), which would be the y component of the triangle formed when the person pulled the cable, and used sin45 to get T. This was not correct.

(To be exact, my calculations were as follows)
Ty = (9.8)(1/2(45.8+6.7) = 33.495 N

sin45= 33.495/T
T=33.495/sin45
T=47.4 N

The answer is neither 33.5 nor 47.4 N. At this point, I don't know how to proceed with the question and I would really, really appreciate help.

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Becca93 said:
(To be exact, my calculations were as follows)
Ty = (9.8)(1/2(45.8+6.7) = 33.495 N
Redo that calculation. That will be the full tension, not the y-component.

Doc Al said:
Redo that calculation. That will be the full tension, not the y-component.

Oh, thank you. Originally thought that the angle was extraneous information and got it wrong, but I obviously did the math wrong.

I have the answer now. Thank you!

## 1. How do you calculate tension in a pulley system?

To calculate tension in a pulley system, you need to first determine the forces acting on the system. This includes the weight of the object being lifted, the force applied by the pulley system, and any other external forces. Once you have the forces, you can use the equation T = F - mg, where T is the tension, F is the force applied by the pulley system, and mg is the weight of the object.

## 2. What factors affect tension in a pulley system?

The tension in a pulley system is affected by several factors, including the weight of the object being lifted, the angle of the rope or cable, and the number of pulleys in the system. The type of pulley (fixed, movable, or compound) also affects the tension. Additionally, any external forces acting on the system, such as friction or air resistance, can impact the tension.

## 3. How does the number of pulleys affect tension in a pulley system?

The number of pulleys in a system can affect the tension in two ways. First, using more pulleys can reduce the amount of force needed to lift an object, thus reducing the tension in the rope or cable. Second, adding more pulleys can also increase the length of the rope or cable, which can increase the tension due to the weight of the rope itself.

## 4. Can the angle of the rope affect tension in a pulley system?

Yes, the angle of the rope can affect the tension in a pulley system. As the angle of the rope or cable increases, the tension also increases. This is because a larger angle means the force applied by the pulley system needs to be greater to counteract the weight of the object being lifted.

## 5. How can you adjust tension in a pulley system?

To adjust tension in a pulley system, you can change the force applied by the pulley system or change the number of pulleys in the system. You can also change the angle of the rope or cable to increase or decrease tension. Additionally, you can use different types of pulleys, such as compound pulleys, to reduce the amount of force needed to lift an object, thus reducing tension in the system.