Can a 2700 N Force Along r2 Free a Crate from Quicksand?

[Peacefulchaos]

Homework Statement

A crate is stuck in quicksand. The man trying to get the crate out of the quicksand thinks that a force of 2700 N applied in the direction r2 will be sufficient to get the crate free. The crate also has a cable attached to it that is connected to a mechanical crank in the direction r1. The cable can withstand up to 4500 N of force before snapping.

r1 = <400, 1200, 300> m
r2 = <-4, 8, -2> m

Will the man be successful in getting the crate out of the quicksand?

Homework Equations

unit vector = position vector / magnitude of position vector

The Attempt at a Solution

I found the unit vectors for r1 and r2, but I'm not sure what to do next. I can convert F1 and F2 to Cartesian components using the unit vectors and their magnitudes, but how can I determine if the crate moves without knowing its weight?

Thanks for any help.

 

[Peacefulchaos]

I solved this on my own. For some reason I thought the problem was stating that F2 directed along r2 was an additional force (another force pulling it out, or something pushing from behind). It was actually saying the crank needed to produce that much force in the r2 direction, which is understandable.

So to solve this problem you would find the force that the crank produces along the r2 vector. To do this you would use the properties of the dot product. I.e., the dot product between F1 (force of crank) dot the unit vector of r2. If this is greater than the necessary 2500 N, then the crate will move (which it is).