Chapter 1 Homework

Homework H4.S – Sp 26

6 Comments
Problem statement
Solution video

DISCUSSION THREAD

Discussion and hints
Recall the following four-step plan outline in the lecture book and discussed in lecture:

Step 1: FBDs
Draw a free body diagram of the system made up of B, bar AB and the spring.

Step 2: Kinetics (angular impulse/momentum and work/energy)
Note that all forces on the system act at the fixed point O. What does this say about the angular momentum of the system about point O? Also, consider the work/energy equation for the system.

Step 3: Kinematics
The kinematics of P are best written in terms of polar coordinates R and φ.

Step 4: Solve
Solve for the R and φ components of velocity of P from these equations.

Any questions?

6 thoughts on “Homework H4.S – Sp 26”

  1. Should we include the particle B, rod OA and spring in the FBD? Then there would be no force driving the rotation? Or should it be just the rod OA and particle B?

    1. Yes, include all three in your FBD. There is nothing that is driving the rotation. Therefore the system that you chose here, both angular momentum about O and mechanical energy are conserved (you see this from looking at your FBD).

  2. I am confused about the direction of the radial velocity. It seems to me like it can be both positive or negative by the work equation since the magnitude is the same.

    1. You raise a good question.

      Mathematically, when you take the square root of a number, you can choose either the “-” or the “+” root. As you say, either is valid since they come from a number that is squared.

      Physically, both the positive and the negative roots make sense. The positive root of R_dot corresponds to the first passing of P at R = L/2 + b asP moves outward. Beyond that passing, the spring will reach a point of maximum compression, and P will then start to move inward toward O. When P reaches the point of R = L/2 + b on the return, this would correspond to the negative root for R_dot.

      In summary, the “+” and “-” roots are both physically and mathematically realizable; they just correspond to two different directions possible for R_dot in the motion of P. You can provide either answer here in your solution.

      Let me know if this is not clear.

  3. I’m slightly confused about how to set up the work energy equation for this problem. Is the T1 of the equation considered to be 0 since the problem states the particle B is not moving relative to bar OA, or is it found using the given w_1 value and the position of B on bar OA?

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