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PHY 113 C General Physics I 11 AM – 12:15 PM TR Olin 101 Plan for Lecture 17: Review of Chapters 9-13, 15-16 Comment on exam and advice for preparation

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PHY 113 C General Physics I 11 AM – 12:15 PM TR Olin 101 Plan for Lecture 17: Review of Chapters 9-13, 15-16 Comment - PowerPoint PPT Presentation


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PHY 113 C General Physics I 11 AM – 12:15 PM TR Olin 101 Plan for Lecture 17: Review of Chapters 9-13, 15-16 Comment on exam and advice for preparation Review Example problems. Webassign questions – Assignment #15

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PHY 113 C General Physics I

11 AM – 12:15 PM TR Olin 101

Plan for Lecture 17:

Review of Chapters 9-13, 15-16

Comment on exam and advice for preparation

Review

Example problems

PHY 113 C Fall 2013 -- Lecture 17

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Webassign questions – Assignment #15

Consider the sinusoidal wave of the figure below with the wave function y = 0.150 cos(15.7x − 50.3t)

where x and y are in meters and t is in seconds. At a certain instant, let point A be at the origin and point B be the closest point to A along the x axis where the wave is 43.0° out of phase with A. What is the coordinate of B?

PHY 113 C Fall 2013 -- Lecture 17

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Webassign questions – Assignment #15

A transverse wave on a string is described by the following wave function. y = 0.115 sin ((π/9)x+ 5πt)

where x and y are in meters and t is in seconds.

Determine the transverse speed at t = 0.150 s for an element of the string located at x = 1.50 m.

(b) Determine the transverse acceleration at t = 0.150 s for an element of the string located at x = 1.50 m.

PHY 113 C Fall 2013 -- Lecture 17

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Webassign questions – Assignment #15

A sinusoidal wave in a rope is described by the wave function

y= 0.20 sin (0.69πx + 20πt)

where x and y are in meters and t is in seconds. The rope has a linear mass density of 0.230 kg/m. The tension in the rope is provided by an arrangement like the one illustrated in the figure below. What is the mass of the suspended object?

T

mg

PHY 113 C Fall 2013 -- Lecture 17

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Comment about exam on Tuesday 10/29/2013

PHY 113 C Fall 2013 -- Lecture 17

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iclicker question

  • What is the purpose of exams?
    • Pure pain and suffering for all involved.
    • To measure what has been learned.
    • To help students learn the material.
    • Other.

PHY 113 C Fall 2013 -- Lecture 17

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Advice on how to prepare for the exam

    • Review lecture notes and text chapters 9-13,15-16
    • Prepare equation sheet
    • Work practice problems
  • Topics covered
    • Linear momentum
    • Rotational motion and angular momentum
    • Gravitational force and circular orbits
    • Static equilibrium
    • Simple harmonic motion
    • Wave motion

PHY 113 C Fall 2013 -- Lecture 17

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What to bring to exam:

  • Clear head
  • Calculator
  • Equation sheet
  • Pencil or pen

PHY 113 C Fall 2013 -- Lecture 17

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iclicker question:

Have you looked at last year’s exams?

A. Yes B. No

PHY 113 C Fall 2013 -- Lecture 17

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Linear momentum

    • What is it?
    • When is it “conserved”?
    • Conservation of momentum in analysis of collisions
    • Notion of center of mass

PHY 113 C Fall 2013 -- Lecture 17

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Linear momentum -- continued

Physics of composite systems

PHY 113 C Fall 2013 -- Lecture 17

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Example – completely inelastic collision; balls moving in one dimension on a frictionless surface

PHY 113 C Fall 2013 -- Lecture 17

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Examples of two-dimensional collision; balls moving on a frictionless surface

PHY 113 C Fall 2013 -- Lecture 17

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The notion of the center of mass and the physics of composite systems

PHY 113 C Fall 2013 -- Lecture 17

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Finding the center of mass

PHY 113 C Fall 2013 -- Lecture 17

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Rotational motion and angular momentum

    • Angular variables
    • Newton’s law for angular motion
    • Rotational energy
    • Moment of inertia
    • Angular momentum

q

PHY 113 C Fall 2013 -- Lecture 17

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Moment of inertia:

PHY 113 C Fall 2013 -- Lecture 17

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CM

CM

PHY 113 C Fall 2013 -- Lecture 17

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iclicker exercise:

Three round balls, each having a mass M and radius R, start from rest at the top of the incline. After they are released, they roll without slipping down the incline. Which ball will reach the bottom first?

C

B

A

PHY 113 C Fall 2013 -- Lecture 17

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q

How can you make objects rotate?

Define torque:

t = r x F

t = rF sin q

r

F sin q

q

F

PHY 113 C Fall 2013 -- Lecture 17

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Example form Webassign #11

  • iclicker exercise
  • When the pivot point is O, which torque is zero?
      • A. t1?
      • B. t2?
      • C. t3?

t3

X

t2

t1

PHY 113 C Fall 2013 -- Lecture 17

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Vector cross product; right hand rule

PHY 113 C Fall 2013 -- Lecture 17

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From Newton’s second law – continued – conservation of angular momentum:

PHY 113 C Fall 2013 -- Lecture 17

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Example of conservation of angular momentum

PHY 113 C Fall 2013 -- Lecture 17

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Fundamental gravitational force law and planetary motion

    • Newton’s gravitational force law
    • Gravity at Earth’s surface
    • Circular orbits of gravitational bodies
    • Energy associated with gravitation and orbital motion

PHY 113 C Fall 2013 -- Lecture 17

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Universal law of gravitation

 Newton (with help from Galileo, Kepler, etc.) 1687

PHY 113 C Fall 2013 -- Lecture 17

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Gravitational force of the Earth

RE

m

Note: Earth’s gravity acts as a point mass located at the Earth’s center.

PHY 113 C Fall 2013 -- Lecture 17

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REM

F

Stable circular orbit of two gravitationally attracted objects (such as the moon and the Earth)

v

a

PHY 113 C Fall 2013 -- Lecture 17

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m2

R2

R1

m1

Circular orbital motion about center of mass

v2

CM

v1

PHY 113 C Fall 2013 -- Lecture 17

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m2

R2

R1

m1

v2

L1=m1v1R1

L2=m2v2R2

L = L1 + L2

v1

Note: More generally, stable orbits can be elliptical.

PHY 113 C Fall 2013 -- Lecture 17

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Gravitational potential energy

Example:

PHY 113 C Fall 2013 -- Lecture 17

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Analysis of static equilibrium

Meanwhile – back on the surface of the Earth:

Conditions for stable equilibrium

PHY 113 C Fall 2013 -- Lecture 17

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X

**

T

Mg

mg

PHY 113 C Fall 2013 -- Lecture 17

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Some practice problems

PHY 113 C Fall 2013 -- Lecture 17

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From webassign:

A 100-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.800 rev/s in 2.00 s? (State the magnitude of the force.)

view from top:

F

R

PHY 113 C Fall 2013 -- Lecture 17

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From webassign:

A 10.3-kg monkey climbs a uniform ladder with weight w = 1.24  102 N and length L = 3.35 m as shown in the figure below. The ladder rests against the wall and makes an angle of θ = 60.0° with the ground. The upper and lower ends of the ladder rest on frictionless surfaces. The lower end is connected to the wall by a horizontal rope that is frayed and can support a maximum tension of only 80.0 N.

PHY 113 C Fall 2013 -- Lecture 17

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