# Solving a 2-Mass System Connected by a Rope

• raptik
In summary, the question asks for the tension in a cord connecting two masses of 0.600kg and 2.2kg, respectively, passing over a frictionless pulley. The equations used are F = ma and W = mg. After trying various methods, the correct equation for tension is found to be T = m1a + m1g = m2g - m2a. The final answer is 9.24N.
raptik

## Homework Statement

Two masses M1 = .600kg and M2 = 2.2kg connected by a cord of negligible mass and passes over a frictionless pulley of negligible mass. Assuming that y-axis has a positive upward direction, what is the tension in the cord?

F = ma

W = mg

## The Attempt at a Solution

I first tried to add up the Fg for both masses under the assumption that the opposing force would be the tension.

I then subtracted the larger Fg from the smaller Fg which was also wrong.

I then came upon https://www.physicsforums.com/showthread.php?t=201258" and tried to follow the process discussed there. I tried to solve for a based on the posts discussed in the other thread but was lost on posts 9 and 10 (NEwayz, back to what I did).

I found the equations of the two blocks to be T - m1g = m1a and m2g - T = m2a.
this makes T = m1a + m1g = m2g - m2a.
Plugging in the numbers gives 5.88N + .6a = 21.56N - 2.2a
solving for a gives a = 5.6ms-2
Plugging this back into the T equation gives a T of 9.24N
I then double the T because there is T working on both ends of the rope and get 18.48N.

Last edited by a moderator:
You don't double T. The tension T is acting throughout the rope. It isn't T on one side and T on the other giving 2T total.

I would approach this problem by first identifying all the given information and variables, and then using the relevant equations to solve for the unknown variable, which in this case is the tension in the rope.

Firstly, I would draw a free body diagram for each mass, showing all the forces acting on them. For M1, the forces would be the tension in the rope (T) and the force of gravity (mg), both pointing downwards. For M2, the forces would be the tension in the rope (T) and the force of gravity (mg), both pointing upwards.

Next, I would use Newton's second law, F=ma, to set up equations for each mass. For M1, the equation would be T - mg = ma, and for M2, it would be mg - T = ma. Since the pulley is frictionless and has negligible mass, we can assume that the acceleration of both masses is the same.

Then, I would solve for the tension in the rope by setting the two equations equal to each other and solving for T. This would give me T = (m1-m2)g/2.2. Plugging in the given values, we get T = (0.600-2.2)(9.8) / 2.2 = -10.56N. Note that the negative sign indicates that the tension in the rope is acting in the opposite direction to the assumed positive direction of the y-axis. This makes sense since the rope is pulling upwards on M2 and downwards on M1.

Finally, I would double this value to account for the tension acting on both ends of the rope, giving a final answer of 21.12N for the tension in the rope.

In conclusion, as a scientist, I would approach this problem by carefully analyzing the given information, using relevant equations, and following a systematic and logical approach to arrive at the correct solution.

## 1. How do you solve a 2-mass system connected by a rope?

To solve a 2-mass system connected by a rope, you must first identify the forces acting on each mass. Then, you can use Newton's Second Law (F=ma) to set up equations of motion for each mass. Finally, you can solve the equations simultaneously to find the acceleration and tension in the rope.

## 2. What are the assumptions made when solving a 2-mass system connected by a rope?

The main assumption made when solving a 2-mass system connected by a rope is that the rope is massless and inextensible, meaning it has no weight and does not stretch or compress under tension. Another assumption is that the pulleys, if present, are frictionless and the masses are point masses with all their mass concentrated at a single point.

## 3. Can a 2-mass system connected by a rope have multiple solutions?

Yes, it is possible for a 2-mass system connected by a rope to have multiple solutions. This can occur if there are multiple configurations or arrangements of the system that satisfy the given conditions. In some cases, there may also be a range of possible values for certain variables, leading to multiple solutions.

## 4. How does the angle of the rope affect the solution for a 2-mass system?

The angle of the rope can affect the solution for a 2-mass system in several ways. A larger angle can lead to a larger tension in the rope and a greater acceleration for the masses. It can also change the direction of the forces acting on the masses, which can impact the equations of motion and the final solution.

## 5. Are there any real-life applications of solving a 2-mass system connected by a rope?

Yes, there are many real-life applications of solving a 2-mass system connected by a rope. One example is in elevator systems, where the tension in the ropes and the acceleration of the elevator must be carefully calculated to ensure safe and efficient operation. Other examples include pulley systems in construction and mechanics, as well as various types of weight and tension measurement devices.

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