# Help understanding work

I have this problem:

An object with 800kg mass is lifted up 2.4m by a force $F$. How much work does the Force do on the object (gravity is the only other force acting on the object)?

From what I have learned, $W = F*d$. Does this mean that there are infinite solutions to this problem, since every force greater than 9.81m/s^2*800kg upwards can lift the object 2.4m?

• Yes! Usually when they ask questions like these, they want you to find the minimum possible work done, although :D Jun 29 '15 at 13:07

Yes, there are an infinite number of solutions, though your teacher will want you to choose the most obvious one.

When the force does work on the mass, that work can be converted into two forms:

1. the potential energy of the object
2. the kinetic energy of the object

If you apply a force of $800g$ then once the object has been raised the 2.4m it will still be stationary because the force is only just enough to counteract gravity and there is none left of to accelerate the object. So the kinetic energy will be zero and the only change will be the change in potential energy. This is obviously how your teacher wants you to analyse the problem.

However, suppose the force is $800,000,000,000g$ (there's no special significance to this number other than it's big!). In this case the object will be raised 2.4m, but it will also be travelling at a high speed. The work done will be a lot higher than in the first case because it increases the kinetic energy of the object as well as its potential energy.

Strictly speaking the question should have stated that the object starts at rest and ends at rest 2.4m higher. This would fully specify the problem.

• What are the units of force you are using John? I understand "$m\cdot g$" or "$800 kg \cdot 9.8 m/s^2$" but I am not used to mixing numbers (with unstated units) with symbols (with implied units). Am I just being picky? $800 g$ appears to have units of $m/s^2$. Apart from that, this is obviously the right answer. Jun 29 '15 at 12:30
• @John Rennie Thanks for answering. I have trouble understanding how applying 800g force is the most obvious answer. If i were to apply a force of 800g upwards, wouldn't that result in the object staying still, since gravity counteracts the force upwards. So i would have to apply a force just greater than the weight of the object to lift it up 2.4m. Jun 29 '15 at 12:46
• @Carefullcars: have a look at my answer to How can we move an object with zero velocity? because it addresses exactly this point. In practice we'd apply a force slightly greater than $800g$ to accelerate the object during the first part of the motion and a force slightly less than $800g$ to decelerate the object over the last part. Over the whole trajectory the force would average out to be $800g$. Jun 29 '15 at 13:15