How to find tension of a single object in a pulley system?

In summary: It's m. So the net force is ma = mg. From there, you can solve for a and plug it back into the equation for Ft.In summary, the problem involves finding the tension, Ft, in a system of blocks connected by a rope. The first step is to set the net force equal to the mass multiplied by its acceleration, and then rearrange the equation to solve for a. Once the acceleration is found, it can be plugged back into the equation for Ft to get the final answer.
  • #1
fissifizz
29
2

Homework Statement



LETTER d only [/B]
phsy.PNG


Homework Equations


Fnet = ma

The Attempt at a Solution


So I considered 2m independently and set its net force equal to its gravity minus its tension.

(2m)a = Fg - Ft = (2m)g - Ft

I then rearranged the equation so that Ft = (2m)g - (2m)a = 2m(g-a)

There's no answer key, so I'm not sure if this is correct. I appreciate any assistance with this problem! Thanks!
 
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  • #2
The problem is that your answer contains a. The directions say to express your answers in terms of m and g.

So, you need to find an expression for a in terms of m and g.
 
  • #3
Mister T said:
The problem is that your answer contains a. The directions say to express your answers in terms of m and g.

So, you need to find an expression for a in terms of m and g.

Ah, ok. Since all the blocks are moving in a system, I'm going to assume that the acceleration calculated in letter b will be used.

Fnet = (5m)a = 5mg - 4mg (I hope I'm calculating this correctly)
(5m)a = mg
a = g/5

So time to plug back in: Ft = 2m(g-a) = 2m(g-(g/5))
Ft = 2m(4g/5)
Ft = 8mg/5

It seems like that's it. Was my original methodology correct though?
 
  • #4
fissifizz said:
Ah, ok. Since all the blocks are moving in a system, I'm going to assume that the acceleration calculated in letter b will be used.

What do you mean? The blocks are connected, and the magnitude of their acceleration is the same.

fissifizz said:
Fnet = (5m)a = 5mg - 4mg (I hope I'm calculating this correctly)

The net force is correct, mg, but the whole mass is not 5m.
 

1. What is a pulley system?

A pulley system is a type of simple machine that uses one or more wheels with a groove around the edge and a rope or cable running through the groove. It is used to change the direction of a force, making it easier to lift or move heavy objects.

2. How does a pulley system work?

In a pulley system, one end of the rope is attached to the object being lifted, while the other end is pulled by the person or machine applying the force. As the rope is pulled, it moves through the groove of the pulley, causing the object to move in the desired direction.

3. What factors affect the tension in a pulley system?

The tension in a pulley system is affected by the weight of the object being lifted, the number of pulleys used, and the direction and magnitude of the force being applied. Friction and the weight of the rope or cable can also impact the tension in a pulley system.

4. How can I calculate the tension in a single object in a pulley system?

To calculate the tension in a single object in a pulley system, you can use the formula T = W + (m x a), where T is the tension, W is the weight of the object, m is the mass of the object, and a is the acceleration of the object. You will also need to consider the number of pulleys being used and the direction of the force being applied.

5. Are there any safety considerations when using a pulley system?

Yes, there are some safety considerations to keep in mind when using a pulley system. It is important to make sure that all parts of the system are in good working condition and that the weight of the object being lifted does not exceed the weight capacity of the pulleys. It is also important to wear appropriate safety gear and to use caution when using a pulley system to avoid accidents or injuries.

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