Solving a Frictionless Pulley Problem: Acceleration of m2

[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?

Homework Equations

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.

 

[Doc Al]

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.

 

[kerimek]

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.