Work Done by Torque on Square Plate of Mass M

In summary: You can use that to find the angular acceleration, and then use kinematic equations to find the angle covered as a function of time. From there, you can use the work equation to find the work done by the force. In summary, to find the work done by the force, you can use the equation relating torque and angular acceleration to find the angular acceleration, and then use kinematic equations to find the angle covered as a function of time. From there, you can use the work equation to find the work done by the force.
  • #1
1/2"
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Homework Statement


In the figure shown a square plate of mass M and side of length L
is fixed at the center . The force F makes the square plate rotate.
The force is always perpendicular to the side.
Find the work done by the force.

Homework Equations


Work = torque x θ


The Attempt at a Solution


I considered the moment arm to be half of the diagonal of length L/√2
Then the force acting perpendicular to it will be F/√2
Torque =FL /2 but then how do i find the angle covered?
The book's answer is (3F2t2)/M
 

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  • #2
1/2" said:

Homework Statement


In the figure shown a square plate of mass M and side of length L
is fixed at the center . The force F makes the square plate rotate.
The force is always perpendicular to the side.
Find the work done by the force.

Homework Equations


Work = torque x θ


The Attempt at a Solution


I considered the moment arm to be half of the diagonal of length L/√2
Then the force acting perpendicular to it will be F/√2
Torque =FL /2 but then how do i find the angle covered?
The book's answer is (3F2t2)/M

There is t in the solution but is not stated in the question.
 
  • #3
The torque is constant, so the the angular acceleration is constant. So you can obtain it as a function of time.
 
  • #4
voko said:
The torque is constant, so the the angular acceleration is constant. So you can obtain it as a function of time.

Can please be more elaborate ?
I reaaly appreciated your help,Thanks.:smile:
 
  • #5
I am not sure what else I could say without solving the entire problem. What is the equation relating angular acceleration and torque?
 

FAQ: Work Done by Torque on Square Plate of Mass M

What is torque?

Torque is a measure of the force that can cause an object to rotate around an axis. It is calculated by multiplying the force applied to the object by the distance from the axis of rotation to the point where the force is applied.

How is work done by torque calculated?

The work done by torque is calculated by multiplying the torque by the angle through which it acts. This can be represented by the equation W = τθ, where W is the work done, τ is the torque, and θ is the angle.

What is a square plate of mass M?

A square plate of mass M refers to a two-dimensional object with four equal sides and a uniform distribution of mass. The letter M represents the mass of the plate, which is a measure of the amount of matter it contains.

How is torque related to the work done on a square plate of mass M?

Torque is directly related to the work done on a square plate of mass M, as it is the force that causes the plate to rotate. The greater the torque applied, the more work will be done on the plate.

What factors affect the work done by torque on a square plate of mass M?

The work done by torque on a square plate of mass M can be affected by several factors, including the magnitude and direction of the applied force, the distance from the axis of rotation to where the force is applied, and the angle through which the force acts.

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