Calculating Torque of a Suspended Bar with Tension | Homework Solution

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In summary, the question asks for the torque exerted on a horizontal bar by a cord attached to a wall. The correct formula to use is torque = rF, and since the mass and weight of the bar can be ignored, the answer is DTsin(theta). The torque is zero when the angle with the wall is zero or 180 degrees.
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PrideofPhilly
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More torque yay!

Homework Statement



A horizontal bar with a mass m suspended from one end is held by a cord with tension T, fastened at a distance D from the end of the bar that is attached to a wall with a frictionless pin. What is the torque about the pin exerted on the bar by the cord?

Homework Equations



torque = rF

The Attempt at a Solution



My answer is DTsin(theta.

Am I right or way off?
 
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  • #2


Since they only want the torque from the cord, (you can ignore the mass of the bar and the torque generated from its weight), then your answer is OK.

When the angle with the wall is zero or 180, there is no torque.
 
  • #3




Your answer is correct. The torque exerted on the bar by the cord is equal to the product of the force (tension) and the perpendicular distance from the point of rotation (pin) to the line of action of the force. In this case, the perpendicular distance is Dsin(theta) where theta is the angle between the cord and the bar. Therefore, the torque is DTsin(theta). Good job!
 

1. How do I calculate the torque of a suspended bar with tension?

To calculate the torque of a suspended bar with tension, you will need to know the length of the bar, the angle of the tension force, and the magnitude of the tension force. The formula for torque is: torque = length * tension * sin(angle). Make sure to use consistent units for length and tension.

2. What is the difference between torque and tension?

Torque and tension are both forces, but they act in different ways. Torque is a twisting or rotational force, while tension is a pulling or stretching force. Torque is typically measured in units of force multiplied by distance (such as Nm or ft-lb), while tension is measured in units of force (such as N or lb).

3. Can I calculate the torque of a suspended bar with tension if the bar is not perfectly horizontal?

Yes, you can still calculate the torque of a suspended bar with tension if the bar is not perfectly horizontal. In this case, you will need to use the formula torque = length * tension * sin(angle), where the angle is the angle between the bar and the direction of the tension force. This angle may be different from the angle of the bar itself.

4. How does the length of the bar impact the torque calculation?

The length of the bar is a crucial factor in calculating torque. The longer the bar, the greater the torque will be for a given tension force. This is because the longer the bar, the farther the perpendicular distance between the tension force and the axis of rotation, resulting in a larger torque.

5. Can I use the torque calculation to determine the stability of a suspended bar with tension?

Yes, the torque calculation can provide information about the stability of a suspended bar with tension. If the torque is positive, the bar will rotate in a clockwise direction and is considered stable. If the torque is negative, the bar will rotate in a counterclockwise direction and is considered unstable. A zero torque indicates that the bar is in equilibrium and will not rotate.

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