Problem statements
Solution video - H3.A (a sign error in the solution appears around the 4:10 mark of the video)
Solution video - H3.B
DISCUSSION THREAD
Please post questions here on the homework, and take time to answer questions posted by others. You can learn both ways.
What unit do we use for the force vectors?
I believe it's just unitless and that the force vector should be in terms of T.
We only have to submit H3.B and not H3.A right?
Yes only H3.B is required
for part b, since it only specifies the projection onto cable CD, and not the force vector CD, of Force vector BD, we only use the position vector of CD and not the force vector of CD, right?
That is correct. I used the unit vector of CD for part b (since it is needed for the dot product formula).
It doesn't matter if you're projecting onto cable CD or force CD; they have the same direction, and you will arrive at the same result. The definition of the vector projection includes normalizing the vector being projected onto, the magnitude is irrelevant as long as it's greater than 0.
For parts b and c in the homework, does it just ask for the magnitude of the vector projection or does it ask for the projection to be in vector format (by multiplying the magnitude by the unit vector)? If I wrote both answers for parts b/c, would this be fine?
For parts b and c, they are looking for the vector projection of the force vector onto the opposing cable. You are right that you will need the magnitude of the force vector that is in the direction of the cable where the force is being projected onto, and you will need to multiply that magnitude with the unit vector of the cable where the force is being projected onto. The key word in the question is vector. A vector has both direction and magnitude. Therefore, your answer will be the vector that you get when you multiply the magnitude and unit vector together, but you must show the work of getting the magnitude in order to arrive at the final answer. So yes, include both, but the final answer will be in vector form.
I feel it is better to write the projection in vector form just to be on the safer side. I think it should be completely fine to give both the magnitude and the full vector form.
When all is said and done, you just need the magnitude and componets solved. If you have that, you get full points.
Hey so for parts b and c, I had both vectors have (d^2) terms and wanted to make sure that the "d" that's in the figure refers to an unknown coefficient and not a unit. Anyone know if I shouldn't have a d^2 term in my answer?
The d is not a unit. It is just the variable or the unknown value as you said. the d actually cancels out in the final answers. As you have d in the numerator and sqrt of d^2 in the denominator, as I have seen and understood.
d I believe acts as an uknown measurement of the unit, so if the answer logically includes d^2 it should be fine.
While working through the problem, you should have d in the equations, but it cancels out since we find the magnitude in the denominator. So the final answer shouldn't have d.
I am confused. I do not know whether for part b and c we use the force or the unit vector for the cable of CD and BD respectively
Use the unit vector of CD and BD because you are projecting in the direction of CD / BD. The magnitude of the projection will come from the force vector, Fbd / Fcd, that is being projected
Is there a preference of decimal or fraction form for answers?
I think decimal form is preferred because it's easier to check if the answer makes sense if it's in decimal form.