The following are links to hints and suggestions on the conceptual problems that appear at the end of each chapter in the lecture book. Note that for virtually all of these questions we are not expecting you to just “know” the answer based on your intuition. In each case, instead, you need to perform some simple analysis first, and from this analysis, draw conclusions on the answers.
Our hope is that through such conceptual questions your intuition on dynamics will develop beyond just remembering methods and procedures. You will see similar conceptual questions on your quizzes and exams in this course.
Use these hints to guide you in your conclusions. Please post your comments and questions below regarding these conceptual questions.
For C4.5, I am lost on finding the value for the displacement. Can we assume the length of the cable is d for our analysis?
Yes, at position 1, the length of cable between B and P is d. At position 2, that length is h.
Therefore, point C at the end of the cable moves through distance of d – h.
Why would it not be F(h-d), since h is the upper bound, and d is the lower limit in the integration of F dot dr?
Yes, that is correct.
Just to clarify, the answer is F(h-d)? I do not see that in the answer choices
The main thing to realize is that the work is positive since F is in direction of motion, so if you write F(h-d), then you have to write -F(h-d), which is the same as F(d-h) which is the answer choice discussed
For C3.4, why is the time derivative of k not 0? Wouldn’t k always point out of the page no matter how the arm is oriented?
AB has two components of rotation: Omega and theta_dot. For the instant shown, k points outward perpendicular to the page; however, with the rotation of Omega it does not remain perpendicular to the page. Therefore, k is a moving axis.
Is there an answer key for the conceptual questions?
Please review the hints provided above on the conceptual problems. The importance of the concept problems is the thought process that leads up to the final qualitative conclusion. Giving the answers often short-circuits the development of the reasoning skills needed to answer these questions on the exam.
For C3.3, would the vP/O)rel term be the speed of the cart + the rate of d_dot? And then for the aP/O)rel term would it be d_ddot (in x and y from theta) + v_dot,cart?
(v_P/O)_rel = the velocity of P as seen by the observer
(a_P/O)_rel = the acceleration of P as seen by the observer
The only motion of P seen by the observer is P moving along in the straight tube with a speed of d_dot and a rate of change of speed of d_ddot. Therefore we have the vectors provided in the Hints file for this problem.
Let me know if this is not clear to you.
For C4.12, I am struggling to understand why when working with the forces in the t direction, cos(theta) is used instead of sin(theta).
It appears that the sine and cosine terms in the two linear momentum equations were switched in the HINTS. That has now been fixed.
Thanks for bringing that to our attention.
For c3.5, how did you solve for 4 unknowns with one equation? (ao, ap, and the relative velocity + acceleration)
There are five terms on the RHS of the acceleration equation. Factors that go into those five terms are presented there in the solution. Simply substitute them in.