Unit 4 ==> Real Work Lifting Something

Don't we need to exert more force to lift a mass rather then just equal it's gravitational force?

More force but no more extra work

• In order to lift the bucket, we do in fact have to lift with a force greater than mg, otherwise there would be no net force and therefore no acceleration.
• Let's write this force as F=mg+K where K is the extra bit of force more than the weight force (can be any value greater than zero).
• Now we can imagine breaking down the work we do into two parts
• The work done by the part of our force that balances gravity (let's call it Wg) 
• The work done by the extra part of our force (let's call it WK).
• Considering only the work Wg, then this will naturally be just mg times the distance we lift.
• The extra force K does not go into fighting gravity, but instead into accelerating the bucket, which in turn increases its kinetic energy. So the work WK goes strictly into the bucket's kinetic energy.
• Now we assume that once we're done lifting the bucket, it's now at rest, and thus has no kinetic energy.
• But we know that the bucket should have kinetic energy equal to WK! 
• So this means that in order to bring the bucket to rest, we must have actually done some extra work to slow the bucket back down to rest. 
• And the only way to get rid of a kinetic energy of WK is to do work of −WK. 
• So these two works balance each other out
• And we get that the total work is just Wg. 
• So what this really means here is that the force must vary over the lifting. It has to start as greater than mg to get it moving, but it must end as less than mg to slow it down. This varying force means that the final work ends up being exactly Wg.  
• MIT Professor Lewin evaluates the net work done here at about 6 minutes into his lecture. He also does a demonstration of this activity.