Two pulleys (one is a combination of two cylinders), and hanging mass.

In summary: The torque on the small wheel is the tension in the rope times the radius of the wheel. The torque on the big wheel is the torque on the small wheel plus the torque due to the mass hanging from the rope. In summary, the problem involves two pulleys with different moments of inertia and a mass hanging from the smaller pulley. The acceleration of the mass, tension in the rope, and tension in the belt can be found using dynamics equations and torque equations. The key is to draw free body diagrams for each part of the problem.
  • #1
9997
2
0

Homework Statement


Two pulleys are mounted on fixed axles that have negligible friction. The small pulley has a moment of inertia of 9.0 kgm^2, and is made of up of two cylinders wielded together, one of radius 7.0 cm, and one of radius 15.0 cm. The large pulley has a radius of 41.0 cm, and a moment of inertia of 84 kgm^2; he pulleys are coupled together using a light belt. A 7.00 kg mass hangs from the smaller pulley by a rope that is wound around the smaller cylinder. The system is initially at rest, and the mass is then let go, and begins to fall.

acd69ed9b11c5eedc5b986d90bd6a6e0.png


a) Find the acceleration of the mass.
b) Find the tension in the rope.
c) Is the tension in the belt the same everywhere?

Homework Equations



Dynamics equations (summation of forces).
Torque = Iα

The Attempt at a Solution



e64a9d9c302ead418475a89577af7ba9.png


I'm actually a bit lost. Our textbook is really bad, and I can't seem to figure out how to solve this question. I've looked online for other resources, but can't seem to find any.

Any help is appreciated! Thank you.
 
Physics news on Phys.org
  • #2
You are doing well - free body diagrams for each part of the problem.

i.e. for the mass:
mg-T=ma (I like to avoid subscripts)

What to do about the wheels right?
You have the right equation - draw the wheels separately and draw the torques on them.
 

FAQ: Two pulleys (one is a combination of two cylinders), and hanging mass.

What is the purpose of using two pulleys, one being a combination of two cylinders, in an experiment with a hanging mass?

The purpose of using two pulleys, one being a combination of two cylinders, is to reduce the amount of force needed to lift the hanging mass. By distributing the weight of the hanging mass over two pulleys, the amount of force needed to lift it is halved. This allows for more precise measurements and easier manipulation of the hanging mass.

How do the radii of the two pulleys affect the mechanical advantage of the system?

The mechanical advantage of the system is directly related to the ratio of the radii of the two pulleys. The larger the ratio, the greater the mechanical advantage. This means that a smaller amount of force is needed to lift the hanging mass when the pulley with the larger radius is used. However, the trade-off is that the distance that the rope must be pulled will also increase.

What is the relationship between the hanging mass and the force required to lift it using the two pulleys?

The relationship between the hanging mass and the force required to lift it using the two pulleys is an inverse one. This means that as the hanging mass increases, the force required to lift it decreases. This is due to the mechanical advantage provided by the pulley system.

How does friction affect the accuracy of the experiment with the two pulleys and hanging mass?

Friction can introduce errors in the experiment with the two pulleys and hanging mass. The presence of friction between the pulleys and the rope can cause the force required to lift the hanging mass to be greater than expected. This can lead to inaccuracies in the data collected. To minimize the effects of friction, the pulleys should be well-lubricated and the rope should be as thin and smooth as possible.

Are there any limitations to using a pulley system with a hanging mass?

Yes, there are limitations to using a pulley system with a hanging mass. One limitation is that the rope must be able to support the weight of the hanging mass without breaking. Additionally, the pulleys themselves have a maximum weight limit that they can support. If these limitations are exceeded, the pulley system may fail and the data collected may be inaccurate.

Similar threads

System of two pulleys and three masses
Replies
22
Views
4K
Falling mass, additionally accelerated by a rope
Replies
18
Views
708
Newton's Second Law (Pulley Sustem)
Replies
3
Views
1K
Olympiad dynamics problem with 3 masses and a pulley
Replies
17
Views
2K
Experimental Design: Pulley and Mass Hangers
Replies
30
Views
2K
Acceleration of a mass lowered by a motor (Help with Non-Ideal Pulley)
Replies
4
Views
1K
Mass and pulley system (Rotational Dynamics)
Replies
9
Views
2K
Angular Acceleration and Linear Acceleration of a Pulley
Replies
4
Views
1K
How Do You Calculate the Angular Motion of a Pulley System?
Replies
15
Views
2K
Velocity of a block attached to a pulley and cylinder
Replies
10
Views
6K

Hot Threads

Recent Insights

Back
Top