Course Review

Physics 2210Fall Semester 2014

Announcements

● Unit 21 “Simple and Physical Pendula” (Nov 24th)● HW Due 11/25th as usual

● No new material Wednesday November 26th. In-class discussion of problems for last midterm, final exam. ● Unit 22 “Harmonic Waves” Monday Dec 1st

● HW due Sunday December 7th at midnight● Exam 3 (covering thru unit 19) December 3rd

● Unit 23 “Standing Waves and Superposition”, Monday December 8th

● HW Due Tuesday 9th

● Course Review December 10th

● Final Exam (December 16th)

Final Exam Details

● When: Tuesday December 16th, 3:30-5:30 PM.● Where: JFB 101... here!● Allowed materials:

● Formula sheet (provided)● Blue/black pen. Indicate errors by strikethrough● Hand held calculator. Not the one on your

cellphone. ● Straightedge to make neat diagrams

More Details

● Coverage: All Units ● Types of problems: Short answer and workout.● Study recommendations:

● Review homework● Review prior exams● Solve problems, problems, problems...

Formula Sheet:Note that this is posted to

course web page under “supplemental reading”

Final Exam Topics

● Section 1: Linear Dynamics● 1-D Kinematics● Vectors and 2-D Kinematics● Relative and Circular Motion● Newton's Laws● Forces and Free-Body Diagrams● Friction

1D Kinematics

● Basis for much of what follows

● Unlikely there'll be a pure 1D kinematics workout

● But...

1D Kinematics

● Basis for much of what follows

● Unlikely there'll be a pure 1D kinematics workout

● Know graphical interpretation!

Vectors and 2D Kinematics

● Recall rules for adding and subtracting vectors

● Graphical techniques● Arithmetic with

components

2D Kinematics: Projectile Motion

● Independent horizontal and vertical motion

● Horizontal: constant velocity

● Vertical: constant acceleration g

Relative Motion

vAB

= vAC

+ vCB

Newton's Laws

1) An object subject to no net external force is at rest or moving at a constant velocity when viewed from an inertial reference frame.

2) a = Fnet

/m

3) For every action there is an equal and opposite reaction F

AB = -F

BA

Forces and Free-Body Diagrams

● FBD: Tool for generating equations for dynamic systems

● Each object in the system is drawn isolated from all but the forces acting on it.

b) what is the acceleration (magnitude and direction) of m

2?

c) what is the amount by which the spring is stretched from equilibrium?

Final Exam Topics

● Section 2: Conservation Laws● Work and Kinetic Energy● Conservative forces and Potential Energy● Center of Mass● Conservation of Momentum● Elastic Collisions● Collisions, Impulse and Reference Frames

Work-Kinetic Energy Theorem

The net work done on a body is equal to the change in kinetic energy of the body

Formal definition of work(“Force times distance” generalized)

Formal definition of kinetic energy

Work and Kinetic Energy

Conservative Forces, Potential Energy

Work-Energy Theorem

b) If the force f is such that the block will move with constant speed v = 0.1 m/s down the ramp, calculate the work done by the force F if the block travels the length of the ramp.c) Suppose that, while traveling at v = 0.1 m/s down the ramp, at d = 3 meters from the end of the ramp the rope breaks. Use the work-kinetic energy theorem to calculate the speed of the crate when it reaches the bottom of the ramp.

Generalize mechanical energy conservation to conservative systems including springs:

Spring P.E. K.E.

Gravitational P.E.

Circular Motion & Work-Energy Thm

Final Exam Topics

● Section 3: Rotational Dynamics● Rotational Kinematics and Moment of Inertia● Parallel Axis Theorem and Torque● Rotational Dynamics● Rotational Statics● Angular Momentum● Angular Momentum Vector and Precession

You will be given I for basic shapes.

Spring PE

RotationalKE

GravitationalPE

TranslationalKE

I = mir

i

2

= “moment of inertia”

Parallel Axis Theorem

Smallest when D 0

Mechanics Lecture 15, Slide 25

Similarity to 1D motion

Mechanics Lecture 15, Slide 26

b) Calculate the centripetal acceleration of point p, 25.0 seconds after the torque starts being applied.c) Calculate the magnitude of the applied torque, in N*m.

Rotational Statics Procedure:

Balance Forces Balance Torques Solve equations

Final Exam Topics

● Section 4: Applications● Simple Harmonic Motion● Simple and Physical Pendula● Harmonic Waves and the Wave Equation● Waves and Superposition

Simple Pendulum/Harmonic Motion

The simple pendulum shown - consisting of a massless string of length L = 1.0 m and a bob of mass 0.1 kg - is given an initial velocity v

0 = 3.0 m/s to the

right, at an initial displacement

0 = 0. Find:

The position of the pendulum at t = 8 seconds.

The tension in the string at t = 8 seconds.

Mass m

Length L

Waves on a String

● A steel guitar string of length L = 1.2 meters is stretched between two fixed points. The speed of a wave on the string is 550.0 meters/second.

● What are the 1st, 2nd, and 3rd longest wavelengths for standing waves on this string

● What is the fundamental (lowest) frequency of vibration of the string?

● If the tension on the string is doubled, what is the fundamental frequency?

● If the string were replaced with a string of the same material but 3 times the diameter, and held at the same tension, what is the fundamental frequency?