Problem statements
Solution video – H2.A
Solution video – H2.B
DISCUSSION THREAD
HINTS:
Part a) – Write down the position vector from C to B: rCB. The unit vector from C to B is found by uCB =rCB/|rCB|. From this, the force of cable CB acting on the mast is: FCB = FCB*uCB.
Part b) -Worked out in a similar way, with CB to be replaced by CA.
Part c) – Refer to the lecture book for determining the direction angles and direction cosines directly from a unit vector that has been written in component form.
Please post questions here on the homework, and take time to answer questions posted by others. You can learn both ways.
For part b, should CA be considered to be equal to 1 when solving for the unit vector with angles (similar to the Vector Defns – Ex 1)?
To find the unit vector u_CA, you should use the equation: u_CA =r_CA/|r_CA|.
Here, r_CA is the position vector, which can be expressed in terms of its magnitude |r_CA| and the angles θ and ϕ.
When you substitute this into the equation, the magnitude in the numerator and denominator will cancel out, leaving the unit vector expressed purely in terms of the angles θ and ϕ.
I’m a bit confused about how to find the unit vector u_CA. What would be the correct expression for finding r_CA?
For finding the direction cosines, is it essentially just the unit vector component of the angle?
yes, that’s correct
example 1 from the lecture and Example 2.B.2 under Lecture examples solutions tab(blog) will be very useful resource for this problem
I am having trouble visualizing the angle components to figure out if my answer makes sense. I know you have to “move the origin” but how do I know which end of the vector to move the origin to and how do I figure it out from there? Thank you in advance
You can try to take a look at the example video of Example 2.B.2 under Lecture examples solutions tab (as Henry posted) to visualize the direction angles.