# Solving Pulleys and Tension Problems

• Bluesroo
In summary: Good job!In summary, the conversation discusses a simple pulley system with two masses attached by a string over a frictionless wheel. The goal is to find the acceleration and tension in the string. The conversation covers the use of free body diagrams, the equation F=ma, and the concept of tension being equal in a frictionless pulley system. The final solution is found by setting up and solving equations for the forces acting on one of the masses.
Bluesroo
This is incredibly simple, but i cannot remember the formula for tension, which is a show stopper.

## Homework Statement

Simple pulley. Two masses attached with a string running over a frictionless wheel. m1 is 8kg and m2 is 12kg. I need to find acceleration and tension over the string.

## Homework Equations

F= ma
anet= (Fg2-Fg1)/(m1+m2)
T= Fnet1+Fg1 or T= Fnet2-Fg2 (I don't think these are right)

## The Attempt at a Solution

F= ma
Fg1= 8kg* 9.8m/sec^2
Fg1= 78.4N

Fg2= 12kg* 9.8m/sec^2
Fg2= 117.6N

anet= (Fg2-Fg1)/(m1+m2) (at second glance this seems like a faulty equation as well...)
anet= (117.6N-78.4N)/(8kg+12kg)
anet= 1.96m/sec^2

Now I can't find tension because I'm not sure where Fnet comes from (the sum of Fg1 and Fg2?) nor do I have the formula for tension written down... I didn't take very good notes on this (surprise surprise )

Last edited:
Draw Free Body diagram of a object. Then Fnet = ma.

Use your everday experience to reason this one out. Then after you get the base of the problem done the rest is simple math.

Two masses hanging on a frictionless pulley, which why is the system going to accelerate?

Which mass is going to move down, causing the other to move up?

Can you write equations to sum up all the forces on these two masses? F = ma

HINT: The tension is the same for both masses (frictionless pulley).

You should end up with two equations with 2 unknowns. You can solve for this.

What are some efficient ways of solving systems of equations?

Hope this helps, let me know if you're still stuck.

@Bright Wang
I have a free body diagram drawn on my paper. I have the anet part figured out, I created that equation correctly... Thanks for the helping me verify that.

@Jegues
I don't see how I can create two equations... Because tension is the same throughout the string wouldn't there only be one equation that can be used to solve? They are solving for the same number...

The only things I can think of are:
T=(Fg2-Fg1)anet
and
T=(m1+m2)anet

In regards to efficiently solving equations, I think that's how I got myself in this... I don't think I understood the material well enough before I tried to simplify equations and combine things.

What you did at the start, is looking at the rope, and the two boxes as a system. Now can you take the system apart, then you can calculate tension. You only need FBD of 1 object.
I'm going to draw it horizontally for one object

<----Tension---|BOX|--------Force of gravity on the one box------> while ~> accele

Now can you create a equation use "sum of Force" = ma. (Of one object). Just look at the FBD

I think I got it (this is using m2):
Fg2= m*ag
Fg2= 12kg* 9.8m/sec^2
Fg2= 117.6N

Fnet= m*anet
Fnet= 12kg*1.96m/sec^2
Fnet= 23.5N

Fg2-Fnet= T
117.6N-23.5N=T
T= 94.1N

Yes, that's what I got.

## 1. How do I determine the tension in a pulley system?

To determine the tension in a pulley system, you can use the equation T = mg + ma, where T is the tension, m is the mass of the object, g is the acceleration due to gravity, and a is the acceleration of the object. You can also use the concept of conservation of energy, where the total energy of the system remains constant, to solve for tension.

## 2. What are the common types of pulleys in a system?

The most common types of pulleys in a system are fixed pulleys, movable pulleys, and compound pulleys. Fixed pulleys have a stationary axle and change the direction of the force applied. Movable pulleys have a movable axle and reduce the effort needed to lift a load. Compound pulleys combine fixed and movable pulleys to create a mechanical advantage.

## 3. How does the number of pulleys affect the effort needed to lift a load?

The more pulleys in a system, the less effort is needed to lift a load. This is because each additional pulley reduces the amount of force needed to lift the load. However, the distance the rope or cable needs to be pulled also increases with more pulleys, so the work done remains the same.

## 4. Can pulleys be used to change the direction of an applied force?

Yes, pulleys can be used to change the direction of an applied force. By wrapping the rope or cable around the pulley, the direction of the force can be redirected. This is useful in situations where the force needs to be applied in a different direction than the load is being lifted.

## 5. What are some real-life applications of pulleys and tension problems?

Pulleys and tension problems are commonly used in everyday life, such as in elevators, cranes, and construction equipment. They are also used in exercise equipment, zip lines, and rock climbing systems. In addition, pulleys and tension problems are essential in engineering and physics experiments to understand the principles of mechanics and motion.

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