Work against gravity

[Nivvedan]

I read in a book under the definition of power. I’ll give it in the same words.

“Work done does not depend on time. For example, If a person A lifts 10 kg load through 5 ft in 2 minutes and person B lifts the same load through the same height in 1 minute, the work done by both the persons is the same, but the rate at which the work is done is not the same. We say that the second person is stronger and has more power. Thus power is defined as the rate of work done.”

Now since the work done is same and Work = F x s , F x s is same for both A and B. Since the height to which the persons lift the load is the same, the displacement is the same. So F1 = F2. But F = ma. Since the mass of the body is same, a1 = a2.

If the acceleration is the same, then why does A take more time to lift the same body from the ground than B? Has it got something to do with gravity?

Can you please explain this?

[Bignose]

Well, firstly, if the object on the floor started at rest, and then was at rest at the top of the 5 ft height, then no change in velocity, and hence no acceleration (acceleration is the derivative of velocity). But, also, you have to remember that gravity is accelerating objects downward, so to move accelerate it upward, just to counteract gravity.

 

It is sort of counterintuitive idea that force is proportional to acceleration. For example, how do you make your bike go faster? You pedal harder. Daily occurrences make it seem like velocity is proportional to force. But, the bike really is accelerated more by pedaling harder, it is just that the equilibrium between forces changes when you put more force into the bike. I.e. the drag increases at the higher velocity.

 

Re-adjusting your intuition to correspond with a physic-based analysis is a difficult skill, but worthwhile if your goal is to get a greater understanding of the physical world.

[swansont]

Work done is by the applied force, but the acceleration of the object is from the net force. As Bignose has pointed out, this is zero.

 

IOW, the lifting is assumed to take place at constant velocity. No net work is done, but the person lifting does work and so does gravity; these add to zero. We typically call the work of gravity the gravitational potential energy.

[Mr Skeptic]

Also, the distances that the two men apply force is not necessarily the same. The stronger man might basically throw his weight upward, and at the top it slows to a stop due to gravity. So he applies a stronger force over a shorter distance (and for less time). Note that both men actually throw the weight upward to some degree, as gravity, and not the men, is stopping it from moving upward.

 

It would be clearer if the men were pushing a cart forward till they reach the same speed, the one who pushes harder will get done sooner.

[Country Boy]

I read in a book under the definition of power. I’ll give it in the same words.

“Work done does not depend on time. For example, If a person A lifts 10 kg load through 5 ft in 2 minutes and person B lifts the same load through the same height in 1 minute, the work done by both the persons is the same, but the rate at which the work is done is not the same. We say that the second person is stronger and has more power. Thus power is defined as the rate of work done.”

Now since the work done is same and Work = F x s , F x s is same for both A and B. Since the height to which the persons lift the load is the same, the displacement is the same. So F1 = F2. But F = ma. Since the mass of the body is same, a1 = a2.

If the acceleration is the same, then why does A take more time to lift the same body from the ground than B? Has it got something to do with gravity?

Can you please explain this?

The problem does not say anything about acceleration! F= ma is the force necessary to accelerate an object. Obviously, you must accelerate the object in order to get it moving but that could be a very quick acceleration which is over very quickly and does not really contribute anything to the work done. The force necessary to lift an object of mass m AT CONSTANT VELOCITY is mg, the weigth of the object. What's happening here is that A is lifting the object at 5/2 feet per minute and B is lifting it at 5 feet per minute- again, that's velocity not acceleration.

[pioneer]

Work is force X distance. While force is mass X acceleration. So we know the mass and the acceleration due to gravity. One then muliplies this by how much distance, one needs to move the object, against gravity.

 

The units of work are (m) X (d/tt) X (d) or mV2, which is energy. The work needed to move an object against gravity is the same as the energy. If we added too much energy, such that the object exceeded the height needed, the work applied over that distance would still be the same. However, the object will have left over energy, to do more work.