# Solving a Frictionless Pulley Problem: Acceleration of m2

• physicsbro
In summary, the problem involves a 29.3 kg block connected to a 6.70 kg block by a massless string over a frictionless pulley. The pulley has a radius of 0.055 m and a moment of inertia of 0.100 kg·m2. A force of 202.5 N acts on the first block at an angle of 29.7°, with no friction between the first block and the surface. The objective is to find the upward acceleration of the second block. The textbook suggests using the net tension divided by the moment of inertia to find the angular acceleration, but this method did not work. Instead, Newton's 2nd law can be applied to all three objects
physicsbro

## Homework Statement

A 29.3 kg block, m1, is on a horizontal surface, connected to a 6.70 kg block, m2, by a massless string as shown. The frictionless pulley has a radius R = 0.055 m and a moment of inertia I = 0.100 kg·m2. A force F = 202.5 N acts on m1 at an angle θ = 29.7°. There is no friction between m1 and the surface. What is the upward acceleration of m2?

## The Attempt at a Solution

My textbook says that the net tension divided by the moment of inertia would give me the $$\alpha$$ and that multiplied by the radius would give me the acceleration, but it didnt work.

physicsbro said:
My textbook says that the net tension divided by the moment of inertia would give me the $$\alpha$$ and that multiplied by the radius would give me the acceleration, but it didnt work.
That's certainly true, but you'll need the tensions to make use of it. Hint: Apply Newton's 2nd law to both masses and the pulley. Combine those three equations and you can solve for the acceleration.

I would first analyze the given information and equations to understand the problem. The equation given in the textbook is correct, but it may not have worked due to a miscalculation or incorrect substitution of values. I would recommend double-checking the calculations and ensuring that all values are in the correct units.

Additionally, I would also consider the forces acting on the system and use Newton's second law, F=ma, to find the acceleration of m2. The forces acting on m2 are the tension in the string, the weight of m2, and the force F acting on m1. By setting up a free-body diagram and using vector addition, the net force on m2 can be found. From there, the acceleration can be calculated using Newton's second law.

It is also important to note that the moment of inertia of the pulley may affect the acceleration of m2. If the pulley has a significant moment of inertia, it may need to be included in the calculations. I would recommend consulting with a physics professor or using a more detailed equation to account for the moment of inertia of the pulley.

In conclusion, solving frictionless pulley problems can be tricky, but by carefully analyzing the given information, using the correct equations, and double-checking calculations, the acceleration of m2 can be accurately determined.

## 1. What is a frictionless pulley problem?

A frictionless pulley problem is a physics problem that involves a pulley system with no friction, where one or more masses are connected by a string or rope that passes over the pulley. The goal is to determine the acceleration of one of the masses.

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

To solve a frictionless pulley problem, you first need to draw a free body diagram to identify all the forces acting on the masses. Then, apply Newton's second law of motion (F=ma) to each mass to create a system of equations. Finally, use algebraic methods to solve for the acceleration of the desired mass.

## 3. What is the role of a frictionless pulley in solving the problem?

A frictionless pulley is essential in a frictionless pulley problem because it allows the string or rope to move freely without any resistance. This means that the tension force in the string is the same on both sides of the pulley, making the problem easier to solve.

## 4. What are the assumptions made when solving a frictionless pulley problem?

When solving a frictionless pulley problem, we assume that the pulley is massless and frictionless, the string or rope is light and inextensible, and the system is in equilibrium or moving at a constant velocity. These assumptions simplify the problem and allow us to use basic physics principles to solve it.

## 5. How does the acceleration of one mass affect the acceleration of the other mass in a frictionless pulley problem?

In a frictionless pulley problem, the acceleration of one mass is equal in magnitude but opposite in direction to the acceleration of the other mass. This is because the two masses are connected by a string that passes over a pulley, and the tension force in the string is the same on both sides of the pulley. This creates an equal and opposite force on each mass, resulting in equal but opposite accelerations.

Replies
3
Views
1K
Replies
5
Views
1K
Replies
2
Views
1K
Replies
4
Views
1K
Replies
3
Views
1K
Replies
10
Views
3K
Replies
1
Views
1K
Replies
23
Views
2K
Replies
29
Views
4K
Replies
7
Views
8K