# Pulley and cords tension physics

• tristanmagnum
In summary: So to solve for the tension in the cord holding the pulley, you can use the equation T = 2*15.6N = 31.2N.In summary, the tension in the cord holding the pulley in Figure 1 is 31.2N. This is determined by setting up equations for the net force on each mass and taking into account the opposite direction of acceleration for each mass. The tension in the cords below the pulley is 15.6N each, and the net force on the pulley is 0. Drawing force diagrams can help in solving these types of problems.
tristanmagnum
The pulley in (Figure 1) is suspended by a cord C. Suppose that m1 = 1.0kg and m2 = 3.9kg .
Determine the tension in the cord that supports the pulley C after the masses are released and before one hits the ground. Ignore the mass of the pulley and cords.

I'm having trouble getting started please help.

i know the tension connecting the masses is the same i just don't know how to solve for it.

To solve these types of problems, I would always recommend starting by drawing force diagrams. This will help you answer such questions as: What upward force is acting on m1? What downward force is acting on m1? What is the net force on m1? What about m2?

so weight would be the downward force for both m1 and m2 and tension would be the upward force. correct?

Correct. And, as you mentioned earlier, tension (T) is the same for both.

Now set up your equations.

Yenaled said:
To solve these types of problems, I would always recommend starting by drawing force diagrams. This will help you answer such questions as: What upward force is acting on m1? What downward force is acting on m1? What is the net force on m1? What about m2?

would the tension for m1 and m2 be 5.8?

Where are you getting 5.8? That's not the correct answer. How did you set up your equations?

thats the problem i have is getting the equations.

would the first be Fnet=T-mg=ma?

Yes. Do that for both masses.

would the second equation be mg-T=ma or would it be the same as the first?

Technically yes, it would be mg - T = ma. Let "a1" be the acceleration of the first mass and "a2" be the acceleration of the second mass.

We have the equations:
(1) T - m1*g = m1*a1
(2) T - m2*g = m2*a2

Both m1 and m2 undergo the same magnitude of acceleration, but in opposite directions, therefore a2 = -a1.

Thus, equation 2 becomes T - m2*g = -m2*a1
Or, as you put it: m2*g - T = m2*a1

so would T-9.8=a1? correct

would T=15.6N

Yep, that's the answer.

my mastering physics tells me its wrong? is there more to the problem?

Ah, I see. I just re-read the original question: it's "the tension in the cord that supports the pulley". I was confused slightly by the wording of the question, and didn't have access to the problem's diagram.

The net force on the pulley is 0. Draw a force diagram for the pulley; it is acted upon by an upward force (which you are trying to find) and the tensions below it (which you have already solved for).

so tension would be the downward and would upward force be the norma force?

The upward force should be the tension in the cord that holds the pulley up. The downward force is the tensions in the ropes (technically, 2*15.6N since there are two ropes hanging from the pulley). And the net force is 0.

oh okay i get it. the tension in the cord holding the pulleys has to be equal to the tensions of both the cords below to bring the net force = to 0.

Yes. Exactly.

## What is a pulley and how does it work?

A pulley is a simple machine that is used to reduce the amount of force needed to lift an object. It consists of a grooved wheel and a rope or cord that runs through the groove. As you pull down on one end of the rope, the object attached to the other end is lifted up.

## How does the number of pulleys affect the tension in the cords?

The number of pulleys affects the tension in the cords by distributing the weight of the object being lifted among multiple ropes. The more pulleys there are, the less tension is required on each individual rope to lift the object.

## What factors affect the tension in a cord attached to a pulley?

The tension in a cord attached to a pulley is affected by the weight of the object being lifted, the number of pulleys used, the angle at which the cord is pulled, and the friction between the cord and the pulley.

## How does the direction of the pull affect the tension in a cord attached to a pulley?

The direction of the pull affects the tension in a cord attached to a pulley by altering the angle at which the cord is pulled. The greater the angle, the more tension is required to lift the object.

## What is the relationship between tension and load in a pulley system?

The relationship between tension and load in a pulley system is that the tension in the rope or cord is equal throughout the entire system. This means that the tension on one side of the pulley is the same as the tension on the other side, and the load is equally distributed among all the ropes or cords.

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