Pulley problem with moment of inertia

In summary, the problem involves a 28.5 kg block on a horizontal surface connected to a 6.10 kg block by a massless string. A force of 231.3 N acts on the larger block at an angle of 30.5°. The frictionless pulley, with a radius of 0.087 m and a moment of inertia of 0.140 kgm^2, is attached to the end of the surface and the smaller block hangs off of it. The task is to find the upward acceleration of the smaller block. To solve this problem, Newton's second law for linear and rotational accelerations needs to be used.
  • #1
howsockgothap
59
0

Homework Statement


A 28.5 kg block (m1) is on a horizontal surface, connected to a 6.10 kg block (m2) by a massless string. The frictionless pulley has a s R = 0.087 m and a moment of inertia I=0.140 kgm2. A force F = 231.3 N acts on m1 at an angle theta = 30.5°. There is no friction between m1 and the surface. What is the upward acceleration of m2?

m2 is hanging off a pulley that's attached to the end of the surface as m1 is dragged across the surface by force F



Homework Equations



f=ma
I=?


The Attempt at a Solution



Initially I tried ignoring the moment of inertia and solving with just tensions but obviously that is not possible. My main problem is that (as you can see from part 2) I am not sure what equation I should be using in reference to the pulley's moment of inertia.
 
Physics news on Phys.org
  • #2
howsockgothap said:

Homework Statement


A 28.5 kg block (m1) is on a horizontal surface, connected to a 6.10 kg block (m2) by a massless string. The frictionless pulley has a s R = 0.087 m and a moment of inertia I=0.140 kgm2. A force F = 231.3 N acts on m1 at an angle theta = 30.5°. There is no friction between m1 and the surface. What is the upward acceleration of m2?

m2 is hanging off a pulley that's attached to the end of the surface as m1 is dragged across the surface by force F



Homework Equations



f=ma
I=?


The Attempt at a Solution



Initially I tried ignoring the moment of inertia and solving with just tensions but obviously that is not possible. My main problem is that (as you can see from part 2) I am not sure what equation I should be using in reference to the pulley's moment of inertia.
You have correctly identified that you need to use Newton's second law for linear accelerations. What you now need to Newton's second low for Rotations - see: http://hyperphysics.phy-astr.gsu.edu/hbase/n2r.html
 

1. What is a pulley and how does it work?

A pulley is a simple machine that consists of a wheel with a groove for a rope or belt to pass over. It is used to change the direction of a force or to transmit rotational motion. As the rope is pulled, the pulley rotates, causing the load to move in the desired direction.

2. What is moment of inertia and why is it important in pulley problems?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. In pulley problems, it is important because it determines how much force is required to move the load and how quickly it will accelerate or decelerate. The greater the moment of inertia, the more force is needed to move the load.

3. How do you calculate the moment of inertia for a pulley system?

The moment of inertia for a pulley system can be calculated by multiplying the mass of the pulley by the square of its radius. If there are multiple pulleys and the rope is wrapped around them, the moment of inertia can be calculated by adding the individual moments of inertia for each pulley.

4. What is the difference between static and dynamic balancing in pulley systems?

Static balancing refers to the process of balancing a pulley system so that the center of mass is directly above the axle. This ensures that the pulley will rotate smoothly and without wobbling. Dynamic balancing, on the other hand, refers to the process of balancing a pulley system while it is in motion. This is important to prevent vibrations and ensure the system runs smoothly.

5. How do you solve a pulley problem with moment of inertia?

To solve a pulley problem with moment of inertia, you first need to identify all the forces acting on the system and their directions. Then, you can use Newton's second law of motion (F=ma) to calculate the acceleration of the load. From there, you can use the equation for rotational motion (τ = Iα) to determine the torque required to accelerate the load and the angular acceleration. Finally, you can use the equations for work and energy to calculate the work done and the final velocity of the load.

Similar threads

Newton's Second Law (Pulley Sustem)
    • Introductory Physics Homework Help
Replies
3
Views
774
What is the "r" in the moment of inertia?
    • Introductory Physics Homework Help
Replies
13
Views
1K
Olympiad dynamics problem with 3 masses and a pulley
    • Introductory Physics Homework Help
Replies
17
Views
1K
Accelerating pulleys (3 pulleys and 3 masses)
    • Introductory Physics Homework Help
Replies
5
Views
1K
Moment of Inertia with pulley and two masses on a string (iWTSE.org)
    • Introductory Physics Homework Help
Replies
8
Views
7K
Ideal Vs Real Mass Pulley system
    • Introductory Physics Homework Help
Replies
10
Views
3K
Solve Pulley-Mass System: m1=4.00 kg, m2=1.00 kg
    • Introductory Physics Homework Help
Replies
2
Views
918
Friction problem involving a pulley
    • Introductory Physics Homework Help
Replies
10
Views
2K
Object causing another object to move with zero friction
    • Introductory Physics Homework Help
Replies
3
Views
1K
Explain friction in a pulley system
    • Introductory Physics Homework Help
Replies
13
Views
4K

Hot Threads

Recent Insights

Back
Top