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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 Zaslavsky♦ 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? – Dostre 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 Zaslavsky♦ 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
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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

1 Answer

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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? – Dostre May 11 '12 at 5:31
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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

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