How Do You Calculate Torque with Tension and Gravity Forces?

[PhizKid]

Homework Statement

Just identify the torques on the bar by the Tension of the wire and the gravity on the bar, using the hinge as the axis of rotation, then find the horizontal and vertical components of the forces. For simplicity's sake, take theta to be 30 degrees.

Homework Equations

Torque = Ialpha
Torque = Force * radius * sin(angle)

The Attempt at a Solution

I found the radius for r_T, which is the radius of the torque of the Tension on the bar. But I don't know how to find the angles. Also, for the torque of the weight on the bar, there are 2 radii from the force of the weight to the bar (since the bar is part of the axis of rotation). I don't know which distance to use. The radius for the Tension was easy because it's direction in the center of the axis of rotation.

Then I don't know what the horizontal and vertical forces will be. It looks like Weight will be a vertical force, but I don't know what other components there are besides Tension and how to find the vertical and horizontal components of Tension.

 

[Bill Nye Tho]

$\tau$ = r x F

Ʃ $\tau$net = 0

(Counter-Clockwise being my positive reference frame)

The positive torque applied to the beam by the wire will be perpendicular component of Tension at a distance of L (length of the beam)

The negative torque applied to the beam by the weight of the beam will be the perpendicular component of weight at a distance of L/2.


F = ma

Ʃ Fnet = 0

You'll have the horizontal and vertical components of the tension & weight as well as the Fx & Fy forces at the hinge.

 

[PhizKid]

How do you know which direction the force of the hinge is pointing towards?

 

[haruspex]

How do you know which direction the force of the hinge is pointing towards?

If you are taking moments about the hinge, those forces have no ,moment so can be ignored.

 

[Nickie]

It seems like you have a good understanding of the concepts involved in finding torque, but you may be struggling with the application of those concepts to this specific problem. First, let's clarify the angles you are looking for. Theta in this case is the angle between the radius of the torque and the force creating the torque. In this case, theta is 30 degrees for both the tension and the weight. As for the radii, you are correct that there are two radii for the weight on the bar - one from the point where the weight is attached to the bar to the hinge, and one from the center of mass of the bar to the hinge. For simplicity, you can use the radius from the center of mass to the hinge.

To find the horizontal and vertical components of the forces, you can use trigonometry. The horizontal component of the tension force can be found by multiplying the tension force by the cosine of the angle between the tension force and the horizontal axis. Similarly, the vertical component of the tension force can be found by multiplying the tension force by the sine of the angle between the tension force and the vertical axis. The weight force will have both horizontal and vertical components as well, which can be found using the same method.

Once you have the horizontal and vertical components of the forces, you can use the equation Torque = Force * radius * sin(angle) to find the torque for each force. Remember to use the appropriate radius for each force.

I hope this helps clarify the steps needed to find torque in this problem. It is important to carefully consider the angles and radii involved, and to use trigonometry to find the horizontal and vertical components of the forces. Good luck with your calculations!