Calculus 3: Find magnitude of force needed for 100 J torque

[chucknorrisfish]

A wrench .9m long lies along the positive y-axis, and grips a bolt at the origin. A force is applied in the direction of (0,1,3) at the end of the wrench. Find the magnitude of the force in newtons needed to supply 100 J of torque to the bolt.
This is the formula i have:
T=|r x F| Can anybody point me in the right direction?

 

[Deleted member 4993]

Re: Calculus 3

A wrench .9m long lies along the positive y-axis, and grips a bolt at the origin. A force is applied in the direction of (0,1,3) at the end of the wrench. Find the magnitude of the force in newtons needed to supply 100 J of torque to the bolt.
This is the formula i have:
T=|r x F| Can anybody point me in the right direction?

So

write the vector for r

write the vector for F

Then cross-multiply to get T

If you are still confused - write back showing some work and pointing out exactly where you are stuck.

 

[chucknorrisfish]

I think r would be <0,1,3> and the F would be (.9)100

so id have <0,1,3> x <0,90,0>

which gives me -270i?

My problem is that i don't know what R and F are supposed to be. F i'm assuming would be force so i think that should be 100J. But what is r? what does that stand for?

 

[Deleted member 4993]

I think r would be <0,1,3> and the F would be (.9)100

so id have <0,1,3> x <0,90,0>

which gives me -270i?

My problem is that i don't know what R and F are supposed to be. F i'm assuming would be force so i think that should be 100J. But what is r? what does that stand for?

A wrench .9m long lies along the positive y-axis,....

r is the r(adius) of T(orque) and F is the F(orce). Sometimes, r is called the Moment Arm.

In your case,

r = 0.9 j

F = 100 (j + 3 k)

T = r x F = (0.9 j) x (100 j + 300 k) = 270 i