A pulley is moved by a belt and turns trough an angle of 420degrees while a point on the belt moves 16 feet. Find the radius of the pulley to the nearest foot

Question

anonymous · Answer

@RadEn This is my last problem, and i have no idea, if its not too much trouble, can i get one last bit of help?

e.mccormick · Answer

Did you try and sketch it?  That can help you know what values go where.

anonymous · Answer

I guess i'l try that, do you know how to do it though?

e.mccormick · Answer

Yes.

e.mccormick · Answer

Know the relationship between revolutions and degrees?

anonymous · Answer

360 in one revolution

e.mccormick · Answer

Good.  Now, know the circumference formula?

anonymous · Answer

2 pi R

anonymous · Answer

how would i connect circumference and degrees here?

e.mccormick · Answer

Ah, the circumfence is the distance of one revolution, or 360 degrees.

e.mccormick · Answer

So you know what one revolution is, the formula for the circumference, the angle moved, and the measure moved for that angle.  Can you set up a ratio with those four things?

anonymous · Answer

I'm not seeing how the 16 feet is going to play in here

e.mccormick · Answer

It is a distance, just like the circumference is a distance.  So you have two distance measures and two degree measures.  Each distance is related to a degrees:

$\dfrac{\text{Distance}}{\text{Degrees}}$

anonymous · Answer

so 16/420, thats half the ratio

e.mccormick · Answer

Yes.  And the other?

anonymous · Answer

the radius/360?

e.mccormick · Answer

Not the radius.  The circumference.

anonymous · Answer

ooooh

e.mccormick · Answer

$\dfrac{16}{420}=\dfrac{2\pi r}{360}$

Then solve for r.  $\ddot \smile$

anonymous · Answer

i get that, but what am i going to do with these two

anonymous · Answer

oh

anonymous · Answer

so, 16/420, then times 360, then divide by 2 and pi?

e.mccormick · Answer

See, you are measuring the distance twice on the same circle.  That is why this works.  Because they are the same circle, they MUST have an equal ratio.

e.mccormick · Answer

That would work.  I might simplify before I did the rest, but it is all personal choice at that point.

anonymous · Answer

all right, thanks :D

e.mccormick · Answer

Where a sketch can help in this situation is it would let you see that you had one pulley and the distance around it.  That let me know what I had to work with.  Everything else is just math principals after that.

Have fun!

anonymous · Answer

yeah, a whole sheet of this same stuff.. its gonna be a blast!