Is This Image Correct for Working from a Constant Force?

[nightshade123]

[SOLVED] work from a constant force

Homework Statement

i can't figure out the answer to hint 2

Homework Equations

w = f deltar

w = F cos theta (deltar)is this img right?

 

[Doc Al]

Your diagram looks good to me. Now how will you make use of it to find the dot product $\vec{F}\cdot\vec{L}$?

 

[nightshade123]

thats what i have been trying to figure outi have tried to relate angles and got

sin (theta*PI/180)* tan (theta*PI/180)

 

[Doc Al]

This should be in your text, but look here: http://hyperphysics.phy-astr.gsu.edu/Hbase/vsca.html"

 

[nightshade123]

well the only reason i didnt say it was

cos ( theta * PI /180)

nor it is like cos ( (theta - 180) * PI /180)

because that is the wrong answer so i don't know wth they want..

and yes that's in my text i have been looking through it the whole time, not examples seem to be like this nor does my book explain this well at all

 

[Doc Al]

$$W = F L \cos \phi$$

Express this in terms of $\theta$.

 

[nightshade123]

I know how to set it up that's is not what i am trying to figure out,

im trying to express PHI in terms of THETA, u see my IMG where it says FIND THIS i can't find that angle, i know how my FINAL answer is going to be expressed.

i can't figure out the how to answer the HINT 2: questionit will be cos ( of some stuff in here * pi /180)

 

[Doc Al]

Hint: $\phi + \theta =$ ?

(Note: The angles are already in radians.)

 

[nightshade123]

180..

i have tried cos ( (180 - theta) * (PI /180))still wrong

 

[Doc Al]

The angles are in radians, so no need to convert to radians:

$$\phi + \theta = \pi$$

Now find $\cos\phi = \cos(\pi - \theta)$

(Review your trig identities if you need to.)

 

[nightshade123]

in rads it would = PI..

 

[nightshade123]

phi = pi - thetai have never seen that before in my life..

 

[nightshade123]

thanks for your help

 

[Doc Al]

So... what's your final answer?

 

[nightshade123]

L*F*cos(PI-THETA)

what threw me off is how they switch between rads and degrees and they are liek don't forget to convert even whe nyou don't need to convert... and whe nyou haev to convert they dotn tell you to convert and when u submit the wrong answer they say, oh you don't forget to convert.. so i assumed it was in degrees and well it was in rads go figure, threw off my answer big time, and when i went to submit my answer in the hint they told me to "not forget to switch to radians" screwey system

 

[Doc Al]

L*F*cos(PI-THETA)

OK, but you can simplify it a bit further using a trig identity. (And get rid of that $\pi$.)

 

[nightshade123]

-cos(theta)

 

[Doc Al]

-cos(theta)

Exactly!