How Much Force to Apply When Doubling the Distance of a Mass on a Stick?

[The_Journey]

Homework Statement

You're holding a massless stick with a mass (m) on it at a distance (d) from your hand. You move the mass to 2d from your hand, how much larger force do you have to apply with your hand to keep the stick stable if the force you were applying before was F?

Homework Equations

Torque = r cross F.
Torque = Rotational inertia * angular acceleration

The Attempt at a Solution

Since you have to apply the same torque as gravity is on the mass, it should be twice the force because:
r * (2F) = (2r) * F.

But my teacher said since Rotational Inertia = m * (r)^2, the force you have to apply have to be 4 times as before because m * (2d) ^ 2 is 4 times as the rotational inertia before.

Can any1 tell me if it's twice or quadruple, with work?

 

[aim1732]

I don't understand your question. How do you hold a massless stick with weight at one end with just one hand? With origin at the point of application of F. there is just the reaction of the normal force(=mg) on the stick. Unbalanced?

 

[The_Journey]

I don't understand your question. How do you hold a massless stick with weight at one end with just one hand? With origin at the point of application of F. there is just the reaction of the normal force(=mg) on the stick. Unbalanced?

Like a ruler or a meter stick. Except the distance is d. You're holding the stick at the end without the weight. The weight is on the stick. You're applying a force with your hand to create a torque that is equal but opposite to the torque created by gravity on the other end so the stick would not rotate. My question is just that if you move the weight further, like to 2d, would you have to double or quadruple the force you were holding with before? My initial thought was that you have to double the force, but my teacher said you have to quadruple so I'm kinda confused.

 

[aim1732]

I pretty much understood that. My point is that with origin at the point of application of force the force due to the mass has an unbalanced torque (the force you apply has no torque about its own point of application so no amount of force can make the rod stable).

 

[The_Journey]

Wait, I forgot that a finger like an index finger is making a fulcrum at a distance d1 from your thumb, so your thumb is applying the force downward for the torque. The mass is at d2 from the fulcrum.

 

[aim1732]

Well even I could be wrong. Just make sure you tell me if you find out more about it.