A force F = (6î - 2ĵ) N acts on a body while it is displaced by d = (3î + 5ĵ) m.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
- A force acts on a body while it is displaced by . How much work does the force do?
- A force acts while the body moves . How much work now?
Need a reminder? The key ideaShow
The work done by a steady force is , in joules. It is positive when the force helps the motion, zero when the force is at right angles to it, and negative when it opposes it. From parts: .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Multiply matching parts and add.
Step 1. (a) .
Step 2. (b) The force has only a part and the motion only an part: .
Answer: (a) . (b) : the force is at right angles to the motion.
Check. In (a), the part of the force opposes the part of the motion, so it subtracts. That is why the total is smaller than .
Watch out. Keep the minus signs. Dropping the sign of gives .
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