Work Lifting Things With and Without Torque

[Cardinalmont]

If I lift a 1kg broom stick 1m when holding it from its center of mass, I will have done 9.8J of work and the broomstick would have gained 9.8J of potential energy. If I were instead to lift it from one end I would have to exert a much larger force due to torque. Lifting this same 1kg broomstick 1m from the end would still give it the same 9.8J of potential energy, but my body would use more energy to do it. Where does this extra energy go?

Thank you.

 

[mfb]

If I were instead to lift it from one end I would have to exert a much larger force due to torque.

Usually the force will be smaller, but it depends on what exactly you do.
In general both the force and the distance change to raise the center of mass by 1 m. Larger force -> smaller distance and vice versa.

 

[Delta2]

It is unclear your exact setup of how exactly you will lifting the stick from the edge.
Depending on the setup, if there is extra energy needed it goes to rotational kinetic energy of the stick.

 

[Cardinalmont]

I apologize for not being clear enough with my question. In both scenarios, the stick will remain completely horizontal during the lift. It is objectively more difficult to lift a broomstick from the side than it is to lift it from the middle given that the broomstick remains completely horizontal in both scenarios, yet both scenarios will give the broomsticks the same change in gravitational potential energy. In both cases, the broomsticks will undergo the same exact motion over the same distance, but my body would have to exert a larger force to lift it from the side.

Upon further reflection I suppose all the extra energy wouldn't actual go into lifting the object but instead into stopping the object from rotating. Theoretically, my question turned to "why does holding something require energy even though no work is bing done?"

I found that answer here
https://physics.stackexchange.com/q...ng-up-cost-energy-while-no-work-is-being-done

I think I get it now. The energy just goes into continuously contracting your muscles which eventually will just become heat.

 

[Delta2]

Well if I get it correctly now, your setup is that you grab the stick with the palm of one hand and lifting it up while keeping it horizontally at the same time.
The mechanics involved when you grab it with your palm, become a bit more complex. Hard to explain it without doing a figure ( I can't do at the moment, sorry) but what happens in this case, is that the torque of the force from your palm, has to counter the torque of weight. The torque of the weight is big because the c.o.m is some distance from your palm.

The torque of the palm force is small, because the palm force is distributed along your palm (and your fingers), and has small distance from the edge of your palm, which edge is the point with respect to which we calculate the torques.

So mathematically it will be (from equality of torques so that there is no rotational motion and the stick remains horizontal)

$Bd_B=Pd_P (1)$

where $P$ is the palm force, $B$ the weight, $d_B,d_P$ the distances of c.o.m and the palm force from the edge of your palm. Because $d_P$ is much smaller than $d_B$, $P$ has to be much bigger than $B$ , if we want equation (1) to hold.

 

[mfb]

Your palm still uses the same amount of energy to lift the broom. In addition you need your muscles to hold the broom that way - human muscles use energy even if they don't move (don't do work), the energy goes into heat in the muscles.

 

[sophiecentaur]

If the stick doesn't rotate on the way up, no extra work is done on it. However, any action involving muscles can't be treated in such a simple way. We use energy just keeping an object suspended because of how our body works. Muscle fibres are constantly stretching and contracting inside our body and that Work corresponds to (wasted) energy.