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# No work when angle is 90 degrees but WHY?

I'm confused about a certain topic: so w=fcosd but why is it when it's at a 90 degree angle (going straight up) there's no work? I get the math - how cos = 0 degrees, but i don't get it in terms of real-life. If you're lifting a heavy object straight up, aren't you applying a force (your hand which is lifting it) and displacement (how high it eventually goes)? Thanks.

### 5 Answers

- kuiperbelt2003Lv 79 years agoFavorite Answer
if the angle between the force applied and displacement is 90 degrees, then the force is doing nothing to cause the displacement

when you lift a heavy object, the angle between the force applied and displacement is zero...

work is the product of the force causing the displacment x the displacement

for instance, if I hold a book stationary in my palm but walk horizontally 20 m, I have walked 20 m but have done no work on the book since the force I applied was not responsible for the displacement of the book

- 9 years ago
It's not cos(d) of the x plane. Its the displacment of the direction its moving in. So when you are moving the object up, the force is in the same direction of the displacement, so therefore cos would be of cos (180) which is 1

- ColfaxLv 59 years ago
because the energy taken from the object by gravitational force when it was going up, will be put back by gravity when the object is coming down, so the object still has the same number of energy, no transfer of energy because gravity is conservative force just like spring force.

since work = change in kinetic energy - change in potential energy, there was no change.

- ?Lv 59 years ago
...It's mathematics. It's just like saying "infinity, i don't understand it in the real world yet it's defined in mathematics."

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