# Pulley problem with frictionless ropes

• Taz.
In summary, the conversation is about finding the acceleration and tension in a system with a frictionless pulley and massless ropes. The homework equations used were the sum of forces equaling mass times acceleration. The students attempted to solve the problem by drawing free body diagrams and setting up equations for each weight, but made an error in one of the equations.
Taz.

## Homework Statement

In the diagram, the pulley is frictionless and the ropes are massless. You are given that m1 = 10.0 kg and m2 = 29.5 kg.

Calculate the acceleration of m2 downwards.

What is the magnitude of the tension in the string?

sum of F= M*A

## The Attempt at a Solution

I tried doing a free body diagram and solving for A but I still can't find the tension...

You should post a picture of the pulley layout to make the problem clear.

OK, you have written Newton's Law. Draw a free body diagram of each weight calling the tension in the rope T. You should have two equations. Let's see them.

m2:

force of tension going up
force of gravity going down

t1-w=ma

m1: same thing ...
t1-w=ma

Let's use some subscripts because the masses/weights are different:

T - w1 = m1 * a

T - w2 = m2 * a

Looking at what you've written, you'll need to define what w1 and w2 are. Also, you have a single variable for acceleration. But the accelerations are in opposite directions so what must be done?

So I have w1 and w2 and I have m1 and m2. Whats missing is T and A. Can I just solve for A or T ?

Taz. said:
So I have w1 and w2 and I have m1 and m2. Whats missing is T and A. Can I just solve for A or T ?

Yes you can but if you do you'll get an incorrect result. You have an error in one of your equations. Acceleration, like 'g', has a direction associated with it.

Signing off for today.

## 1. What is a pulley problem with frictionless ropes?

A pulley problem with frictionless ropes is a common physics problem that involves using pulleys and ropes to lift or move objects. In this type of problem, the ropes are assumed to have no friction, meaning they can move freely without any resistance.

## 2. How do you solve a pulley problem with frictionless ropes?

To solve a pulley problem with frictionless ropes, you need to first draw a diagram to visualize the setup. Then, apply the principles of conservation of energy and Newton's laws of motion to set up equations and solve for the unknown variables. This often involves using the concept of mechanical advantage, which is the ratio of the output force to the input force.

## 3. What are the assumptions made in a pulley problem with frictionless ropes?

The main assumption made in a pulley problem with frictionless ropes is that the ropes have no friction. This means that the tension in the rope is the same throughout, and the rope does not stretch or bend. Other assumptions may include the weight of the ropes and pulleys being negligible and the pulleys being massless.

## 4. How does adding friction to the ropes affect the solution of a pulley problem?

Adding friction to the ropes can significantly affect the solution of a pulley problem. Friction causes the tension in the rope to vary, and it also introduces a torque, which can change the rotational motion of the pulleys. This makes the problem more complex and may require additional equations to solve.

## 5. Can real-life pulley systems be frictionless?

In theory, it is possible to create a frictionless pulley system. However, in reality, there will always be some amount of friction present, no matter how small. This is because all materials have some degree of roughness, and when in contact, they will produce some friction. Therefore, frictionless ropes and pulleys are an idealized concept used in physics problems, but not achievable in real life.

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