# Simple Tension Problem: Calculating Tension and Acceleration

• physicsnewb7
In summary, the conversation discusses the tension and acceleration of two masses suspended by a frictionless string on a frictionless pulley. The tension is solved for using Newton's second law and the total mass of the system, resulting in an acceleration of 1/7g. Alternatively, the string can be imagined as straight and the acceleration can be calculated using conservation of energy.
physicsnewb7

## Homework Statement

Two masses are suspended by a frictionless string on a frictionless pulley, one with mass 75 kg and the other 100 kg.
What is the tension of the string and the acceleration of the masses

## The Attempt at a Solution

My attempt was to say since mass A, 75 kg, was 75 percent of mass B, then the acceleration of mass B would be 25 percent of the acceleration of gravity 9.8 m/s^2.
so it would be roughly 2.5 m/s^2. Since the acceleration was 2.5 m/s^2, I thought the tension would be equivelant to the force of the mass of both A and B times the acceleration 2.5 m/s^2 ie. F=ma. Clearly there is something wrong with this approach. What is it that I'm missing? is there a generalized formula for tension of a string?

physicsnewb7 said:
Two masses are suspended by a frictionless string on a frictionless pulley, one with mass 75 kg and the other 100 kg.
What is the tension of the string and the acceleration of the masses

Hi physicsnewb7!

Call the tension T, and then apply good ol' Newton's second law twice (to each mass separately) …

since the acceleration, a, of each mass is the same (in opposite directions), you can solve for T and a

so if a I say a100kg=100g-T and a75=T-75g, where a is the acceleration, g is gravitational acceleration and T is tension, then add the two equations together to get a=25/175g=1/7g and then solve for T by plugging a in the equations. Is that right? would the acceleration be 1/7g? any help would be greatly appreciated!

physicsnewb7 said:
so if a I say a100kg=100g-T and a75=T-75g, where a is the acceleration, g is gravitational acceleration and T is tension, then add the two equations together to get a=25/175g=1/7g and then solve for T by plugging a in the equations. Is that right? would the acceleration be 1/7g? any help would be greatly appreciated!

Hi physicsnewb7!

Yes, that's right!

Another way of doing it is to imagine that the string is straight …

there's 100g of force pulling it left, and 75g pulling it right, making a total of 25g … since the total mass is 175, that makes a = 175g/25 = g/7.

(or, if you're not interested in the tension, you could even use conservation of energy and a = dv/dt = v dv/dh = 1/2 d(v2)/dh)

Thank you so much TinyTim for responding and helping.

## 1. What is a very simple tension problem?

A very simple tension problem is a physics problem that involves calculating the force of tension in a rope or string. It typically involves two or more objects connected by a rope or string and the force exerted by the rope on each object.

## 2. How do you solve a very simple tension problem?

To solve a very simple tension problem, you need to first identify all the forces acting on the objects connected by the rope or string. Then, you can use Newton's Second Law of Motion (F=ma) to calculate the force of tension by setting up equations for each object and solving for the unknown force.

## 3. What are some common misconceptions about solving tension problems?

One common misconception is that the tension in a rope or string is always equal to the weight of the object it is supporting. However, the tension can vary depending on the angle of the rope or string and the forces acting on the objects. Another misconception is that the tension is always in the same direction as the rope or string, when in fact it can be in any direction.

## 4. How can I practice solving very simple tension problems?

You can practice solving very simple tension problems by creating your own scenarios with different forces and angles, and then using the equations and principles you have learned to solve for the tension. You can also find practice problems online or in textbooks.

## 5. What real-life applications are there for understanding tension problems?

Understanding tension problems can be helpful in a variety of real-life situations, such as engineering and construction, rock climbing and other outdoor activities, and even in daily tasks like tying knots or lifting heavy objects with ropes. It can also be useful in understanding the stability of structures and objects under different forces.

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