Announcements : Announcements Team Names
Exam III on Wednesday
Camera Status
Practice, Practice, Practice
Advising
HW10 - In-Class
HW11 - Keep until Monday
Chapter 10 : Chapter 10 Newton’s Laws
Class Question : Class Question How do units differ from variables?
List 10 clear examples of units and 10 clear examples of variables.
Class Objectives : Class Objectives Learn the relationship between position, velocity, and acceleration
Learn and apply Newton’s First, Second, and Third Laws
Learn some secrets of Calculus
What are the Forces of Nature? : What are the Forces of Nature? Gravitational Force
Electromagnetic Force
Electrostatic and Magnetic
Nuclear Force
Strong and Weak
Friction
Spring
Tension
Push
Newton’s First Law : Newton’s First Law Law of Inertia
Newton’s 1st Law : Newton’s 1st Law Law of Inertia
“Bodies remain at rest or in uniform motion in a straight line unless a net force acts on it.”
Thought Questions
Why don’t planets move in straight lines?
Would they move it straight lines if there were no gravitational force? Newton’s Cannon
Newton’s Second Law : Newton’s Second Law SF = m a
“The amount of acceleration that a force produces depends on the mass of the object being accelerated.”
Newton’s Second Law : Newton’s Second Law Example Questions:
What happens to acceleration if the force is doubled?
Answer:
….if the mass is double?
Answer:
Newton’s Third Law : Newton’s Third Law Action-Reaction
“Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body.”
Newton’s Third Law - Action/Reaction : Newton’s Third Law - Action/Reaction Action-Reaction Table
Wall
Gravity
Earth & Moon
Gravity : Gravity Universal Gravitational Force Inverse Square Law G = 6.67 10-11 N·m2/kg2
Gravity Questions : Gravity Questions Did the Moon exert a gravitational force on the Apollo astronauts?
What kind of objects can exert a gravitational force on other objects?
The constant G is a rather small number. What kind of objects can exert strong gravitational forces?
Gravity Questions : Gravity Questions If the distance between two objects in space is doubled, then what happens to the gravitational force between them?
Find the gravitational force between a 90-kg person and the Earth using the inverse square law (Equation 10-37) and Table 10.6. Show your work and include units for your answer.
Chapter 10 : Chapter 10 Newton’s Laws
Definitions : Definitions Vector Quantity
a quantity that has both magnitude and direction
Vector
an arrow drawn to scale used to represent a vector quantity
Scalar Quantity
a quantity that has magnitude but not direction
Vector or Scalar? : Vector or Scalar? Speed………..
Velocity……...
Acceleration..
Time………….
Force…………
Distance…….. scalar
vector
vector
scalar
scalar
it depends...
Some Definitions : Some Definitions Position - a location usually described by a graphic on a map or by a coordinate system
Some Definitions : Some Definitions Displacement -- change in position,
where
Example : Example Write an expression for each vector below and find their magnitudes.
Vector Notation : Vector Notation Position Vector
Unit Vectors
Magnitude
Team Exercise 4.4
Some Definitions : Some Definitions Average velocity
rate of position change with time
Some Definitions : Some Definitions Instantaneous Velocity
Some Definitions : Some Definitions Speed
the magnitude of instantaneous velocity
Example : Example Suppose that your drive around in a circle in a parking lot at 30mph.
Consider the instant that your car is facing north.
What is your speed?
What is your instantaneous velocity ?
What is average velocity?
Some Definitions : Some Definitions Average Acceleration - rate of velocity change with time
Instantaneous Acceleration
Derivatives : Derivatives The derivative is associated with the slope of a function.
Some Derivatives : Some Derivatives Powers
Trig Functions
Exponentials
Example : Example Assume that r(t)=kt where k is a constant.
Plot r versus t.
Plot v versus t.
Plot a versus t.
Write an equation for v(t) and a(t).
Example : Example Assume that r(t)=Ct3 where C is a constant.
Plot r versus t.
Plot v versus t.
Plot a versus t.
Write an equation for v(t) and a(t).
Example : Example Assume that r(t)=rosin(wt) where ro and w are constants.
Plot r versus t.
Plot v versus t.
Plot a versus t.
Write an equation for v(t) and a(t).
Example 10.1 : Example 10.1 Assume that you...
walk at 3mph for 15 minutes,
then drive at 40mph for 2 hours, and
then ride a bike at 10pm for 45 minutes.
Plot v versus t.
Plot r versus t.
Do you differentiate or integrate to get r(t)?
Integrals : Integrals The integral is associated with the area under the curve.
Some Integrals : Some Integrals Powers
Trig Functions
Exponentials
Example : Example Assume that a(t)=k where k is a constant.
Plot a versus t.
Plot v versus t.
Plot r versus t.
Write an equation for v(t) and r(t).
Newton’s Second Law (A second look) : Newton’s Second Law (A second look) A non-zero net force will cause a mass to accelerate.
The time-rate-of-change of momentum is proportional to the net force on the object.
Newton’s 2nd Law for Constant Mass : Newton’s 2nd Law for Constant Mass If mass is constant then
Problem 10.2 : Problem 10.2 A motorcycle moves with an initial velocity of 30m/s.
When its brakes are applied, it decelerates at 5.0m/s2 until it stops.
Plot the position, velocity and acceleration as a function of time.
What is the position, velocity and acceleration 2 seconds after the brakes are applied?
Multiple Directions : Multiple Directions The equations of motion can be written for each direction independently.
Velocity
Position
Problem 10.3 : Problem 10.3 A girl shoots an arrow upward.
It strikes the ground 10.0 seconds later.
What was its initial velocity and what was the maximum height?
Problem 10.4 : Problem 10.4 A bullet is fired vertically into the air and reached a maximum height of 15,000ft.
What was the initial velocity?
What assumptions must be made?
Problem 10.5 : Problem 10.5 A man standing on a 200-ft tower throws a ball upward at 40 ft/s.
How long does it take to hit the ground?
Chapter 10 : Chapter 10 Newton’s Laws
Announcements : Announcements Homework 12 due on Wednesday.
Remember to get advising.
Project Two is due on December 6th.
That’s next week today.
Project Two : Project Two Scoring:
1 Point for each inch that the projectile travels.
Instructions:
See course home page
Homework 12 : Homework 12 http://www.physics.sfasu.edu/astro/OnlineExams/FCI/fci_main.html
Kinematic Equations Where did they come from? : Kinematic Equations Where did they come from?
Calculus Basics : Calculus Basics Derivative
Indefinite Integral
Definite Integral
Constant Acceleration : Constant Acceleration Equation of motion is
The o in v subscript refers to the original or initial value at the beginning of the time interval of interest. Integrate both sides where acceleration is constant.
Slide51 : Arranging this equation
Substituting the velocity equation from the previous page Integrating both sides
Coil Gun : Coil Gun Final Exam Question
How fast must the projectile be traveling when it leaves the straw if it is to travel 100 inches horizontally?
Newton’s Laws -- Review : Newton’s Laws -- Review First Law
Interia
Second Law
F=ma
Third Law
Action/Reaction Law of Gravity
Team Exercise, 3 min. : Team Exercise, 3 min. The derivative of velocity with respect to time is:
position or acceleration
By integrating velocity with respect to time we get:
distance traveled or acceleration
The derivative of position with respect to time is:
acceleration or velocity
Integrating acceleration twice with respect to time is :
velocity squared or distance
The derivative is associated with the _________ while the integral is associated with _________
area under the curve, slope
Homework 12 : Homework 12 5. According to Newton’s Second Law, what is the net force on a 2000-lb car if it travels at a constant 60mph for 2 hours?
Homework 12 : Homework 12 6. A 1500-kg automobile has a projected frontal area of 1.9 m2 and a drag coefficient of 0.35. It is traveling at 100km/h on a flat road when suddenly both the engine and brakes fail. What is the drag force on the automobile at the moment the brakes fail? The density of air is 1.3 g/liter.
Homework 12 : Homework 12 Will the drag force increase, decrease or stay the same as time goes by?
What would the drag force be if the medium was water rather than air?
Problem 10.7 (modified) : Problem 10.7 (modified) Assume that a projectile is fired upward at an angle and that air resistance is negligible.
Find y as function of x instead of time using the equations below.
What is the shape of the projectiles path?
Team Exercise (3 minutes) : Team Exercise (3 minutes) One dimensional motion
What is the distance traveled in 3 seconds?
What is the acceleration at 1.25 hours?
Exercise - Newton’s Laws : Exercise - Newton’s 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 ball 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)
Solution : Solution Step 1: Draw a Picture
Solution (cont’d) : Solution (cont’d) 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?
Solution : 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 (velocity); rather, forces cause accelerations (change in velocity).
Today’s Demos : Today’s Demos Inertia
Lead Brick and Hammer
Inertia Bars
Disk and Ring Race
Rotating Platform
Metronome
Balancing A Meter Stick
Rotation Adds Stability
Bicycle Tires
Moving Water
Spin Guns Center of Mass
State of Texas
Curious George
Next Week
Bed of Nails
Fluid Flasks
And more....
Trebuchet Problem (Modified 10.6) : Trebuchet Problem (Modified 10.6) The projectile is fired at an angle of 35° relative to the ground.
It is fired with a velocity of 100ft/s.
Find the following:
vxo and vyo
axo and ayo
How long was the projectile in the air?
How high did it go?
How far did the projectile go?
Section 10.3 - Forces : Section 10.3 - Forces Forces are vector quantities. What is the magnitude of this force?
Problem 10.1 : Problem 10.1 A car starts from rest and travels northward.
It accelerates at a constant rate for 30 seconds until it reaches a velocity of 55mph.
Plot the acceleration, velocity and position as a function of time.
Next Chapter… : Next Chapter…
Locate Homework 12 : Locate Homework 12 Take 3 minutes to answer questions 1, 2 and 3.
Project Two – The Trebuchet : Project Two – The Trebuchet
Final Trebuchet Tweaks : Final Trebuchet Tweaks Consider a trough
Weight and test your trebuchet
Allow for hole and pin adjustments
Prepare for rain
The Ideal Trebuchet Problem : The Ideal Trebuchet Problem In the absence of air resistance, a projectile fired at an angle of 45° will have a maximum range.
What initial speed must a projectile have in order to have a range of 20 yards?
...of 40 yards?