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Lecture 5: Newtonian Dynamics
September 5, 2017
Reading Assignment
- Read: Chapter 5; Supplementary Reading CH 1
- Study: Exs 5.1, 5.2, 5.4, 5.5, 5.6, 5.11
- Ignore: Exs 5.8, 5.9, 5.10 (we'll discuss static friction, but we won't use $\mu_s$)
Objectives
- (Continuing objective) Relate concepts of classical mechanics to “everyday” situations and discuss various applications of the concepts to practical problems in various fields of science, medicine and engineering.
- Given a physical situation, apply Newton's Second and Third Laws following these steps: a) sketch the situation, b) identify the forces, c) draw free-body (force) diagrams for each relevant object in the system (separate from original sketch), d) write Newton's Second Law for x-, y- and z- components for each mass (each component is a separate equation), and e) solve for unknowns.
- Solve problems involving weight forces, normal forces, tensions, spring forces, friction forces, and drag forces.
- Given the initial position and velocity of an object acted on by a force in one dimension, use the numerical iteration method to calculate the position and velocity several time increments later.
Homework
- Wednesday's Assigned Problems:
A15, A16, A72; CH 5: 3, 14, 21, 25, 27, 37, 45; Supp CH 1: 1
Answers: CH 5 #14 $4.0\, \hat{\imath} + 1.7\, \hat{\jmath} \,\text{N}$.
Notes: For CH 5 #3, use free-body diagrams and Newton's Second Law to justify your answer.
- Monday's Hand-In Problems: A14, A17, A18; CH 5: 36, 38, 46; CH 6: 22, 30, 40; Supp CH 1: 2
Lecture Materials
- Click here for the Lecture overheads
or here for full-sized versions.
Answers to conceptests: (1) 6; (2) 1; (3) 5; (4) 3; (5) 5
- Click here for step-by-step approach to Newton's law problems.
- Excel sheet with example calculation for numerical method.
Videos of example problems
To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.- Video Example #1 A problem involving friction and tilted coordinate systems. Basically Video Example #1 from Lecture 3, but with friction. ans: $\tan(\theta)$
- Video Example #2 Circular motion in a vertical circle. Similar concepts to twirling a bucket of water over your head. ans: (a) $v_\text{min} = \sqrt{gR}$ (b) $N = 2mg$, up
- Video Example #3 Another example of circular motion, but harder. ans: $$T_\text{top} = \frac{1}{2}\left( \frac{mv^2}{R\cos 45^\circ} + \frac{mg}{\sin 45^\circ}\right)\quad T_\text{bottom} = \frac{1}{2}\left( \frac{mv^2}{R\cos 45^\circ} - \frac{mg}{\sin 45^\circ}\right)$$
Pre-Class Entertainment
Relevant toy of the day
Actually, this is relevant for both Newton's second law (today) and for conservation of energy (next week).While cleaning my office (!), I re-discovered a great toy that I had forgotten. #PhysicsOfBeverages #ComingSoonToPHYS211 #thespillnot.com pic.twitter.com/W9AQgzcdnM
— Tom Solomon (@TheChaoticBird) August 17, 2017