How Is the Mass of a Board Determined Using Torque and Tension?

In summary: T--The rope is connected .2m from the left end. A weight of 3kg hangs from the left end of the board. What is the mass of the board?In summary, the mass of the board is 2kg.
  • #1
andy7793
5
0
Missing template due to originally being posted in a different forum
Hi All,

I'm confused with a particular question and I'm not entirely sure how the answer was derived.

A one-meter board with uniform density hangs in static equilibrium from a rope with tension T--The rope is connected .2m from the left end. A weight of 3kg hangs from the left end of the board. What is the mass of the board?
-----> |T=?
__(.2m)___|____________________Board
|
|
3kg

A 1kg
B 2kg <---Answer
C 3kg
D 4kg

Thank you in advance!
-A
 
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  • #2
I'm unable to understand your diagram. Can't you provide something better than that, like, say, a real figure uploaded using the snipping tool?

Chet
 
  • #3
Sorry about that! Here is the diagram and original question posted!

A
 

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  • #4
Please draw a free body diagram of the board, showing all the forces acting on it.

Chet
 
  • #5
I'm not very good at drawing fbd for scenarios like this. Bare with me please &Thank you.
 

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  • #6
And what of the force you are asked to find? Where is the centre of gravity for a board with uniform density?
 
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  • #7
Here is how the problem was reasoned through according to the book:

"The axis of rotation is the point where the rope attached to the board. The hanging weight creates a counter-clockwise torque equal to 3kg x 0.2m. The wight of the board creates a clockwise torque at the distance from the rope attachment to the board's center of mass, which is 0.3m. The net torque is zero, so the clockwise torque equals the counterclockwise torque, so 3kg x 0.2m=0.3m times the weight of the boards. Therefore the wight of the board is 2kg. "

Thank you!
 
  • #8
andy7793 said:
Here is how the problem was reasoned through according to the book:

"The axis of rotation is the point where the rope attached to the board. The hanging weight creates a counter-clockwise torque equal to 3kg x 0.2m. The wight of the board creates a clockwise torque at the distance from the rope attachment to the board's center of mass, which is 0.3m. The net torque is zero, so the clockwise torque equals the counterclockwise torque, so 3kg x 0.2m=0.3m times the weight of the boards. Therefore the wight of the board is 2kg. "

Thank you!
This is a correct analysis. It's too bad you had to refer to the book to get a solution.

Chet
 
  • #9
I know. I struggled with this one, especially with little practice with problems like this--Thank you

A
 

Related to How Is the Mass of a Board Determined Using Torque and Tension?

1. What is torque and tension?

Torque and tension are two important concepts in mechanics that describe the forces acting on an object. Torque is the measure of rotational force applied to an object, while tension is the measure of the force applied to an object in a straight line.

2. How are torque and tension related?

Torque and tension are related through the concept of leverage. When torque is applied to an object, it creates tension in the material, which can cause it to stretch or deform. The amount of tension created depends on the amount of torque applied and the material's strength and flexibility.

3. What are some examples of torque and tension in everyday life?

Torque and tension can be observed in many everyday activities, such as using a wrench to tighten a bolt (applying torque to create tension), stretching a rubber band (creating tension), or opening a door (applying torque to the doorknob).

4. How do scientists measure torque and tension?

Scientists use various tools and instruments to measure torque and tension, depending on the specific application. For torque, a torque wrench or torque meter can be used, while a tension meter or load cell can be used to measure tension.

5. What is the importance of understanding torque and tension in engineering and design?

Understanding torque and tension is crucial in engineering and design as it allows for the proper selection of materials and components for a given application. It also helps in determining the appropriate amount of force and stress that can be applied to a structure or object without causing damage or failure.

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