EXAM 1

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EXAM 1

• Wednesday, October 9, 2002
• See 111 web page for time and location
• Exam will cover all material through class 5.2
  (50 PS, 50GR)
• Review Power Point slides, reading assignments
  and homework.
• Emphasis on learning objectives

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Exam 1

• Exam will consist of
• True/False
• Multiple choice
• Work out
• Drawings (sketching)
• Closed book, notes. Standard cover sheet
  provided.
• Bring pencil and calculator (no restrictions).
• SCANTRON sheets provided.

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Exam 1

• Exams from previous years available at the TEES
  Copy Center, 2nd Floor WERC (building next to
  Zachry - across from P.A. 51)
• Ask for 111 Exams under Kohutek

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Class 5.2

• Analysis of Motion
• Newtons Laws

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Class Objective

• Learn and apply Newtons First, Second, and Third
  Laws
• Unidirectional
• Multidirectional
• Learn the relationship between position,
  velocity, and acceleration

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Some Definitions

• Position -- a location usually described by a
  graphic on a map or by a coordinate system

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Some Definitions

• Displacement -- change in position,
• where

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Some Definitions

• Average velocity - rate of position change with
  time (vector)
• Instantaneous Velocity (vector)
• Speed - the magnitude of instantaneous velocity
  (scalar)

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Average and Instantaneous Velocity (1D)
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Some Definitions

• Average Acceleration - rate of velocity change
  with time (vector)
• Instantaneous Acceleration (vector) -

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Example

• One dimensional motion
• What is the distance traveled?
• What is the acceleration at 1.25 hours?

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Constant Acceleration

• Equation of motion -
• where acceleration is constant
• integrating both sides
• The 0 in v subscript refers to the original or
  initial value at the beginning of the time
  interval of interest.

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Constant Acceleration

• arranging the equation
• substituting the velocity equation from the
  previous page
• integrating both sides
• yields

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Multiple Directions

• Equations of motion can be written for each
  direction independently.
• Velocity
• Position
• where vx and ax are the velocity and
  acceleration in the x direction, respectively
  similarly for the y direction

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Distance, Velocity, and Acceleration

• Suppose a dragster has constant acceleration.
• If a dragster starts from rest and accelerates to
  60 mph in 10 seconds. How far did it travel?
  Assume constant acceleration.

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Plot Speed vs time
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Distances.
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Pairs Exercise

• As a PAIR, take 15 minutes to solve the following
  problem
• A cannon fires a projectile with an initial
  velocity of 1500 ft/s at an angle (relative to
  the ground) at 50o. Assume that the projectile
  lands at a point that is 1200 ft. above that at
  which it was launched. NEGLECT DRAG DUE TO AIR
  RESISTANCE.

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Pairs Exercise (cont.)

• Using Excel determine
• Time of flight
• Range (x coord. at point of impact)
• Maximum height of projectile
• Using Excel, plot trajectory (x vs. y) of
  projectile. Use at least 100 data points from
  point of launch to point of impact.
• SAVE YOUR FILE - YOU WILL NEED IT LATER.

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Hint Projectile Problem - No Drag

• Acceleration
• ax 0 (neglecting drag)
• ay -g (assuming up is positive)
• Velocity
• Vx Vocos(q)
• Vy Vosin(q) - g t

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Hint Projectile Problem - No Drag

• Position
• X Xo Vocos(q)t
• Y Yo Vosin(q)t - 0.5gt2
• All of these equations assume NO DRAG.

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Newtons 1st Law

• Law of Inertia
• Every body persists in its state of rest or of
  uniform motion in a straight line unless it is
  compelled to change that state by forces
  impressed upon it.

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Momentum
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Newtons Second Law

• Law of Forces
• The time-rate-of-change of momentum is
  proportional to the net force on the object.

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Newtons 2nd Law for Constant Mass

• If mass is NOT constant then

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Newtons 2nd Law for Constant Mass

• If mass is constant then

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Newtons Third Law

• Law of opposite reactions
• To every action there is always opposed an equal
  reaction
• or, the mutual actions of two bodies upon each
  other are always equal and directed in contrary
  parts.
• The earth and the moon orbit about a common point
  near the surface of the earth because the earth
  pulls on the moon and the moon pulls on the earth.

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Exercise1 - Newtons Laws

• A pickup truck is moving with a constant speed of
  30 mph along a city street.
• You are sitting in the back of the truck and you
  throw a softball straight upwards at a speed of
  20 mph.
• Neglecting air resistance
• What will be the path of the ball with respect to
  the pickup truck and where will the ball land
  with respect to the truck?
• i.e. what are the x and y values of the peak and
  final positions of the ball?
• Plot the trajectory of the ball assuming fixed
  coordinate system.

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Solution

• Step 1 Draw a Picture

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Solution (contd)

• the ball follows a parabolic path and remains
  directly above the truck at all times.
• Is a horizontal force acting upon the ball?
• Votes for yes?
• Votes for no?

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Solution

• Answer NO. There is no horizontal force acting
  on the ball.
• The horizontal motion of the ball is the result
  of its own inertia. When thrown from the truck,
  the ball already possessed a horizontal motion,
  and thus will maintain this state of horizontal
  motion unless acted upon by a force with a
  horizontal component (Newton's first law).
• Summary forces do not cause motion rather,
  forces cause accelerations.

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Solution (cont.)

• How do we know that the path of the ball is
  parabolic?
• Answer
• Apply the equations of motion in the x and y
  directions
• X Vxot
• Y Vyot 0.5gt2

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Team Exercise

• As a TEAM, you have 5 minutes to answer the
  following questions
• In the real world, can the effects of air
  resistance be neglected in projectile problems?
• Assuming your answer is no, how would air
  resistance affect the trajectory?
• Would the trajectory be affected by the mass of
  the projectile? Size and shape of the projectile?

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Why Newtons Laws?

• Engineers use models to predict things such as
  motion, fluid flow, lift on an airplane wing,
  movement of neutrons in a nuclear reactor,
  deflection of beams or columns, etc.
• Newtons laws are widely used and a good first
  example of engineering models.

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Newtons Law of Gravitation(1687)

• Every particle of matter in the universe
  attracts every other particle with a force that
  is directly proportional to the masses of the
  particles and inversely proportional to the
  square of the distance between them.

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Newtons Law of Gravitation

• In equation form
• Fg magnitude of gravitational force on either
  mass
• m1, m2 mass of body 1 and body 2, respectively
• r distance between the center of mass of body 1
  and body 2
• G Universal gravitational constant

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Newtons Law of Gravitation

• For objects located on the surface of Earth
• m1 mE mass of Earth
• r rE radius of Earth (mean value)
• G 6.67 X 10-11 N.m2/kg2 (constant)

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Newtons Law of Gravitation

• Let
• and
• So that
• or
• Where weight of a body with mass,m
• 9.806m/s2 32.174 ft/s2

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Assignment 8

• TEAM ASSIGNMENT - Project
• Due10/9/02
• FOUNDATIONS 10.1, 10.4, 10.5, 10.8, 10.9