Calculating Acceleration of a Falling Bucket Attached to a Pulley System

  • Thread starter the whizz
  • Start date
  • Tags
    Beam Mass
In summary, the problem involves a bucket of mass m connected to a frictionless pulley of mass M. The goal is to find the equation for the acceleration of the bucket when it is released from rest and allowed to fall. By using Newton's 2nd law for torques and forces, the following equations can be derived: ma = mg - T and T*R = I*alpha, where T is the tension, R is the radius of the pulley, and I is the moment of inertia. Solving these equations leads to the final equation for the acceleration of the bucket.
  • #1
the whizz
32
0

Homework Statement


1.A bucket of mass m is connected by a rope to a frictionless pulley of mass M. Use Newton’s 2nd law for torques and Newton’s 2nd law to find an equation for the acceleration of the bucket if it is released from rest and allowed to fall.



Homework Equations





The Attempt at a Solution



so i need we need to find Normal force in both direction. i know that

sum of Force in X direction is that o= N- Tcos(theta)

From the problem i am not sure how to find the Tension and where the normal force in the Y direction would come from.
 
Physics news on Phys.org
  • #2
Isn't what you have is a F = m*g being retarded by an I*a/R where I is the moment of inertia?

Apparently the frictionless part refers to the rotation of the pulley and not the friction of the rope on the pulley because if the rope is free to slip, what torque would there be?
 
  • #3
Take the tension T to be the reactant force

Hint...it is 90 degrees to the axis of rotation.
 
  • #4
Forces acting on the bucket are T and mg. Since bucket is moving downwards, net force acting on it is
ma = mg - T...(1)
The tangential force actin on pulley is T.
Therefore The torque on pulley is T*R = I* alpha = I*Ra ...(2)
Substituting the expression for I and solving eq. 1 and 2 , find the equation for the acceleration.
 

What is the purpose of hanging a mass from a beam?

The purpose of hanging a mass from a beam is to study the effects of gravity on the mass and the beam. This can help determine the strength and stability of the beam and its ability to support weight.

How does the mass affect the beam?

The mass hanging from the beam creates a force known as weight, which pulls down on the beam. This weight puts stress on the beam and can cause it to bend or deform. The greater the mass, the greater the force and potential for deformation.

What factors can affect the results of hanging a mass from a beam?

There are several factors that can affect the results of hanging a mass from a beam, including the material and shape of the beam, the type and placement of support structures, and the location and distribution of the mass on the beam.

What is the difference between static and dynamic hanging of a mass from a beam?

Static hanging involves suspending a mass from a beam and measuring its effect on the beam while it remains in a stationary position. Dynamic hanging involves adding motion to the hanging mass, such as swinging or bouncing, to observe how it affects the beam.

How can the results of hanging a mass from a beam be applied in real-world situations?

The results of hanging a mass from a beam can be applied in various engineering and construction scenarios. This can include determining the appropriate materials and support structures for building bridges, buildings, and other structures, as well as designing equipment to safely lift and transport heavy loads.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
672
  • Introductory Physics Homework Help
Replies
10
Views
3K
  • Introductory Physics Homework Help
Replies
17
Views
1K
  • Introductory Physics Homework Help
Replies
22
Views
3K
  • Introductory Physics Homework Help
Replies
30
Views
1K
Replies
25
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
908
  • Introductory Physics Homework Help
Replies
8
Views
5K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
1K
Back
Top