# About the angle between force and displacment, W=F.d cosƟ

1. Jan 9, 2015

### Sculter

• HW Template missing as it was moved from another forum
W=F.d cos Ɵ, in a problem Ɵ=30, but in the solution he used Ɵ=60, and vice versa in other problems, can anyone explain why?

Last edited by a moderator: Jan 9, 2015
2. Jan 9, 2015

### Staff: Mentor

Is θ the angle between F and d, or is it something else? Please post the full problem so we know what you're talking about.

3. Jan 9, 2015

### Sculter

problem like:

*calculate the force acting on an object if the work done to move it a distance 50m equal 2500J and if the angle between the force and the perpendicular to motion is 30
the answer: w=fd cosθ , F=2500/50xcos60 = 100N

*a man of mass 70kg. goes upstaris of lenth 50m. calculate the work done if g=10m/s2 http://im88.gulfup.com/rmDnTK.png [Broken]
-answer W=Fd cosθ, 70x10x50 x cos30

-problem with no changing in angles-

*a force of 100N acts on an object and moves it a distance 2.5m, calculate the work by the force if the force is inclined by an angle 60 on the direction of motion
answer: W=100x2.5x cos60= 125J

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i don't know why he changes angles and when, i think i'm missing something.

Last edited by a moderator: May 7, 2017
4. Jan 9, 2015

### Staff: Mentor

Note that the angle given is not between F and d, but between F and the perpendicular to d. It's up to you to figure out the correct angle!

Again, the angle given is the angle of the stairs with the horizontal. What you need is the angle between the force (gravity) and the displacement.

Here they just give you the required angle, so you can just plug it in.

To use the work formula you need the angle between the force and the displacement. Sometimes you'll be given that angle directly; other times you'll have to figure out the correct angle to use.

5. Jan 9, 2015

### Sculter

oh, great now i know why, i didn't realize it, thank you
but how do i find the angle?

6. Jan 9, 2015

### Staff: Mentor

You are welcome.

Start by drawing yourself a diagram. And use the properties of right triangles. (For example, the two angles of a right triangle are complementary. They add to 90 degrees.)

7. Jan 9, 2015

### Sculter

Thanky you very much!
Your really helped me