Problem V: Tension & Forces on a Rotating Rod | Homework Solution

[Nash77]

Homework Statement

V. See the diagram attached --> problem V.

A 1-kg mass rod has a length of 1 m and is attached to a vertical wall at point Q. The rod is free to rotate around Q. The other end of the rod (P) is tied with a string fixed to the wall. The system is at rest. Take g=10 m/s2 if needed.
1) Find the tension force exerted by the string on the rod.
2) Find the force exerted by the wall (at the point Q) on the rod.
3) If you suddenly cut the string, the rod will swing down. Find the linear velocity (V) of the point P just before the rod hits the wall (the momentum-of-inertial I=(1/3)ML2 if the rod rotates about the end point Q. L is the rod length and M is the rod mass).

Homework Equations

sum of forces in y direction = 0 (because at rest)
Forces are Tension (up) and Weight=mg (down)
I = (1/3)ML^2
Torque = I*alpha

The Attempt at a Solution

1) I said the tension force must be equal to the weight since the rod is at rest,
so weight = mg = 1*10 = 10 N. So tension = 10 N.
2) Is there a force exerted by the wall? I thought all of the forces were being exerted in the vertical direction, but if the wall exerts a force at Q it would be in the horizontal direction. Does this mean there is no force exerted??
3) I = 1/3*1*1^2 = 1/3. So torque would be 1/3*alpha. Is acceleration just gravity? In that case, torque would be 3.333, but then again is torque even related to linear velocity?

 

[Redbelly98]

Okay, I think I found the diagram you refer to in this other post:

https://www.physicsforums.com/showthread.php?p=3186587#post3186587​

Homework Equations

sum of forces in y direction = 0 (because at rest)

True. For a body at rest, and not rotating, this is one of three useful equations. Do you the other two?

Forces are Tension (up) and Weight=mg (down)

You're missing the force exerted by the wall. Also, tension acts at an angle, in the direction along the string -- not straight upward.

I = (1/3)ML^2
Torque = I*alpha

Yes. And what is alpha, for an object at rest?

The Attempt at a Solution

1) I said the tension force must be equal to the weight since the rod is at rest,
so weight = mg = 1*10 = 10 N. So tension = 10 N.
2) Is there a force exerted by the wall? I thought all of the forces were being exerted in the vertical direction, but if the wall exerts a force at Q it would be in the horizontal direction. Does this mean there is no force exerted??

There is a force exerted by the wall. It can have both horizontal and vertical components.

3) I = 1/3*1*1^2 = 1/3. So torque would be 1/3*alpha. Is acceleration just gravity? In that case, torque would be 3.333, but then again is torque even related to linear velocity?

The forces are gravity and the force exerted by the wall (at point Q), so acceleration is affected by both of those. Rather than calculate the acceleration, I'll suggest using conservation of energy to solve this part.