# What is the work done?

A painter uses 1.93kJ of mechanical energy to pull on the rope and lift a 20kg paint barrel at constant speed to a height of 7.5m above the ground. How much work was done lifting the paint barrel?

I know that work input is 1.93kJ and the gravitational potential energy (output) is 1470J, but which is the work done?

• Welcome to physics.StackExchange! Please read the rules: meta.physics.stackexchange.com/questions/714/… on posting homework-like questions. You should show the work that you have tried and then pose the question with what concept you are struggling with. – John M Jul 23 '15 at 3:45
• @JohnM: I believe showing the calculation of the PE change in the barrel is enough to satisfy this. OP has isolated the question to which value is being asked for. – Ross Millikan Jul 23 '15 at 4:20
• I'm with Ross, I think this is a fine if not exciting homework question. A problem understanding which value of work represents work done qualifies as a conceptual question. – David Z Jul 23 '15 at 6:31

The work done by the painter is $1.93$ kJ, which represents the force he applied to the rope times the length of the pull. The work applied to the barrel is $1.47$ kJ. The rest went into friction. I believe the question is ambiguous between the two values, but that is an English question, not a physics one.

• "I believe the question is ambiguous" This. The question is ambiguous. The work done by the lifting agency, or the work done to the load? The former uses the higher value, the latter the lower – dmckee Jul 23 '15 at 4:14

Because the barrel is moving at constant speed. The tension in the rope is equal to the weight of the barrel. So the answer should be your 2nd value.

• So the work done is the energy output not the energy input(total energy applied to lift)? – stacope32 Jul 23 '15 at 2:36
• Yes, for this problem. You should really apply the definition of work. Work of a force is the product of this force and the distance traveled along the force. For this problem, "force" is the tension of the rope. Therefore, the answer is 1470 J. – Drake Marquis Jul 23 '15 at 2:41