For physics teachers
Picture below:
which force does more work on the crate? Explain

Question

anonymous · Answer

|dw:1394407117311:dw| I know that it is F1, because it doesn't have any angle..
I just don't know how to explain it very well. Can anyone tell me how to explain this in order to get full marks? thanks!

anonymous · Answer

Depends on magnitudes of force.

anonymous · Answer

In both cases you would say: $$
W_i=\mathbf F_i\cdot \mathbf r = \|\mathbf F_i\|\|\mathbf r\|\cos(\theta)
$$

anonymous · Answer

In the case of $F_1$ we have $\cos(\theta) =\cos(0) = 1$, which is the highest that it could be.

In the case of $F_1$, we have $ 0<\theta <\pi/2\quad, 0< cos (\theta) < 1$

anonymous · Answer

mean to say $F_2$ for the second one.

anonymous · Answer

hmm.. okay , thanks!

anonymous · Answer

We know that the $cos(\theta)$ component is smaller, so the $F_2$ would need to have a bigger magnitude to over compensate

anonymous · Answer

so which means that $F_1$ will do more work?

anonymous · Answer

Without knowing which force is larger, cannot answer this.

anonymous · Answer

oh, my bad! i'm not looking at the diagram properly! yeah, you guys are right thanks!