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Bill’s job is to lift bags of flour and place them in the back of a truck, which is parked next to him. Sally is loading the same bags of flour into a similar truck that is located 10 m away. Sally wants a raise because she says she is doing more work than Bill. Does the physics definition of work support her claim?

Attempt: By the definition Work is Force multiplied by the Displacement in the direction of the force. Sally does the same amount of Work when she lifts the bag. But, when she cares the bag for 10 m to the truck there is no force exerted on the bag in the direction of the truck. Therefore, she does the same amount of Work. Is my reasoning correct? Why the Force exerted in the direction of the truck is zero?

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Hi Dostre, and welcome to Physics Stack Exchange! Generally we discourage questions that just ask for someone to check your work. Once you have identified the specific concept that you're not sure about, that's the point at which it's appropriate to ask a question here. For example, what reason do you have to think that Sally might be doing more work than Bill? – David Z May 11 '12 at 5:34
Because she cares the bags for a greater distance. I understand what you say. Should I delete the question or just remove my attempt, so the answers will contain the a complete explanation? – Koba May 11 '12 at 5:44
No, it's still a useful question, and if you remove your attempt it would just be a homework question with no work shown (something like that, anyway), which is Very Bad (see the FAQ). Actually, the sentence you added makes it a much better question, since you're now asking about a concept that confuses you, not just asking something which can basically be given a yes/no answer. – David Z May 11 '12 at 6:20
Actually, Sally will lose more energy than Bill. But this additional energy will not go into the energy of bag but into heat (Sally shall be warmer). As you hold bag with your hands, muscles in the hand continuously relax and contract and that requires energy even if you don't move bag at all... – Pygmalion May 11 '12 at 6:28
Note that the definition of work depend on which force we are talking about, e.g., gravitational force, friction force, normal force, etc. If we are talking about the gravitational force, then Yes, the two gravitational works are the same. – Qmechanic May 11 '12 at 10:36
up vote 0 down vote accepted

Yes, your reasoning is correct.

You could also reason this way: the work done by Bill and Sally is turned into energy. In both cases the final energy - potential energy of the bag - is same for both of them.

Edit: after editing, you also asked: "Why the force exerted in the direction of truck equals zero?"

Let's start with a reasonable assumption that bag is carried toward the truck with the constant velocity. In case of constant velocity, according to 1st Newton law, the net forces equals zero. There are only two forces acting on the bag: the force of gravity (vertically down), and the force of Sally (vertically up). Therefore there is no horizontal force in direction of the truck.

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Thanks for timely response. May I edit your answer by adding a graphical representation and short explanations, so others will have a better chance to understand this concept? – Koba May 11 '12 at 5:31
You are always free to edit questions and answer, but they will be reviewed before they are made public. Also, do not forget to accept the answer. – Bernhard May 11 '12 at 5:51
@Pygmalion Could you please explain the reason for Sally getting more tired ? – Vinayak Jan 13 '15 at 16:24
@Vinayak Human body is not a rigid body. When in passive position (e.g., laying on bed) you don't need any energy to maintain mechanical position. However, if you want to keep it in non-passive position (standing, walking, carrying) requires constant turning off and turning on of individual muscles, hence energy consumption. E.g. even just standing still at one place and maintaining physical shape of standing body requires energy! – Pygmalion Jan 14 '15 at 12:29

Sally is correct. Of course they both do the same amount of work lifting the bag, but Sally does additional work moving the bag to the truck. This is because the bag had an initial horizontal velocity of zero. It is not possible to move something at a constant velocity that has in initial velocity of zero. First it will be necessary to accellerate it for some time and distance. Since the object being accellerated has mass, force must be exerted. And since the force must be exerted over some distance, however small, work has been done.

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