Chapter 2: Laws of Motion

Nature, and Nature's laws lay hid in night: God said: “Let Newton be !” and all was light — Alexander Pope (1688-1744), British poet.

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2.1 Newton’s First Law

• Recognize that force is needed to change an object’s motion.

• Explain Newton’s first law.

• Describe how inertia and mass are related.

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Do you need a sustained force to keep moving?

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This is a major difference in our conceptual understanding of nature. Everyday experience says “yes” because of frictional forces surrounding us.

Ideally, the answer is “no”!

Inertia

• Inertia is the tendency of an object to resist changes in its motion.

• Inertia is related to the mass of the object.

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Newton’s 1st Law of Motion

• Taken over from Galileo’s ideas on Inertia.

• “Things in motion tend to stay in motion; things at rest tend to stay at rest.”

• “An object at rest will stay at rest and an object in motion will continue in motion with the same speed and direction UNLESS acted on by a force” – page 29.

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Force

• A force is a push or pull, or any action that has the ability to change motion. Objects in contact with each other usually exert forces on each other, but there are also force fields, e.g., gravity, that exert forces at a distance.

• There can be no change in motion without the presence of a force.

• Force is measured in Newtons (N) in the metric system, or pounds (lbs) in the English system.

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Net Force

• Generally there may be many forces acting on an object at the same time, so we have to consider the net force acting on an object.

• Forces act in different directions, and the direction matters, therefore forces don’t necessarily add like normal numbers.

• Forces up can cancel out forces down, and forces to the right may cancel forces to the left.

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Net Force

Since force has a direction associated with it, we generally use arrows to represent forces.

Equilibrium

• We can think of the net force as all forces acting on an object summed together.

• If the net force is zero, the object is in equilibrium and it’s motion does not change.

• If SF = 0, then the object is in equilibrium – Static (rest)

– Dynamic (constant speed in a straight line)

• If SF ≠ 0, then the object is speeding up or slowing down, or changing its direction!

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Static & Dynamic Equilibrium:

Which one is “dynamic”?

In equilibrium, the net force is equal to zero.

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SF=0

2.2 Acceleration and Newton’s Second Law

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• Define and calculate acceleration.

• Explain the relationship between force, mass, and acceleration.

• Determine mass, acceleration, or force given two of the quantities.

Acceleration

• In Section 2.1, we learned a force causes a change in motion, we call a change in motion an acceleration.

• A car going form zero to 60 mph in 10 seconds will change (increase) its speed by 6 mph every second.

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Three Ways to Accelerate

• We learned earlier that force and velocity have direction. Acceleration also has a direction.

• We will learn later that force, velocity, and acceleration are vectors.

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Acceleration

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Acceleration is the rate of change in velocity. For example, if your acceleration is +50 m/s2, then your velocity is increasing by 50 m/s each second. A deceleration (a slowing down) is mathematically just a negative acceleration.

Newton’s 2nd Law of Motion

• A force causes a mass to accelerate, both the size of the force and the size of the mass determine the acceleration.

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amFF net

S

more inertia!

Applying Newton’s 2nd Law

1. The net force is what causes acceleration.

2. If there is no acceleration, the net force must be zero.

3. If there is an acceleration, there must also be a net force.

4. The force unit of Newtons is based on kilograms, meters, and seconds.

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Calculating Acceleration

• Two objects, A and B, each have two forces acting on them. Which object, A or B, has the greater acceleration?

• What is the net force on A? On B?

• What is the acceleration of A? Of B?

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B has a greater acceleration of 1 m/s2, A has an acceleration of 2/3 m/s2. Both accelerations are to the right!

Force and Energy

• A force will always accompany a transfer of energy.

• Likewise, a force is needed to create an energy difference.

• Generally “systems” prefer to go from a higher energy state to a lower energy state.

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2.3 Gravity and Free Fall

• Describe the motion of an object in free fall.

• Calculate speed and distance for an object in free fall.

• Distinguish between mass and weight.

• Explain how air resistance affects the motion of objects.

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Acceleration due to Gravity

• An object in free fall is under the influence of gravity only – we ignore air resistance.

• At the earth’s surface, the acceleration due to gravity is g = 9.8 m/s2 or ~ 10 m/s2.

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10 m/sec

20 m/sec

Upward Launches

• Technically velocity and acceleration are vectors and have a direction. The acceleration due to gravity is always downward and we will generally call this the negative direction, so -g = - 10 m/s2.

• Velocity will be positive if the object is going up, and negative if the object is coming down.

• Every second in the air, an object in free fall will lose 10 m/s of speed on the way up, and gain 10 m/s of speed on the way down!

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+20 +10 0 -10 -20

Upward Launches

• Note at the very highest point the velocity is momentarily zero, although it is still continuously accelerating!

• If given the initial upward velocity, you should be able to tell the time it will take to get to its highest point, and doubling that, the total time in the air!

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tv

gtvv

atvv

f

if

if

1040

4 seconds

8 seconds

Free Fall and Distance

• We can use the average velocity to help us find the distance (or height) an object falls.

• If the initial velocity is zero, then the average velocity will just be half the final velocity (assuming a is constant).

• Can you find the height of the cliff in this problem?

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Vf =50m/s, Vavg =25 m/s, d =125 m

Free Fall and Distance

• We can also find the maximum height an object is projected up in the air if we know the initial velocity using the same formulas on the previous slide.

• What is the average velocity between the starting point and the highest point?

• What was the time to get to the highest point?

• Multiple the average velocity by time to get the maximum height!

• We can also use the formula d = ½ gt2. 25

20 m/s

4 s

80 m

Weight vs. Mass

• Weight is just the force of gravity on an object.

• The textbook uses Fg, but we will generally use the symbol W for weight.

• Mass is more fundamental than weight, since your weight depends on what planet you are on!

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Weight vs. Mass

27 http://www.youtube.com/watch?v=ToMs7RaL11U&feature=player_embedded

Why do all objects have the same acceleration due to the earth’s gravity, regardless of mass?

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It is true the heavier object has a greater force of gravity on it, but it also has more resistance to a change in its motion – it has more tendency to stay exactly where it is – more inertia!

Air Resistance

• Ideally (and in many cases) we can ignore air resistance, but not always.

• Air resistance depends on the surface area of the object.

• Air resistance also depends on the speed of the object; increased speed causes more air resistance.

• When an object’s speed increases to the point where its weight (down) and air resistance (up) are equal, the object will stop accelerating and it will have reach terminal speed.

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Apollo 15 astronaut David Scott in 1971

30 http://www.youtube.com/watch?v=L55jImEhNZ0

2.4 Graphs of Motion

• Describe motion with position versus time and speed versus time graphs.

• Use a position versus time graph to calculate speed from the slope.

• Use a speed versus time graph to calculate acceleration and distance traveled.

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Distance (Position) vs. Time Graph

• The slope of a line is the ratio of the “rise” (vertical change) to the “run” (horizontal change).

• For “d vs. t” graphs, the slope represents the speed of the object.

• If the plot of the motion is a straight line, then the slope is constant, and so is the speed. What will be the acceleration in this case?

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The acceleration is zero for uniform motion!

Graphs of Accelerated Motion

• If the speed of an object is changing, the slope changes, so the graph curves.

• Graphs for Free Fall and deceleration are shown on this slide.

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Velocity vs. Time Graph

• In general a slope is the change in the vertical variable divided by the change (“rise”) in the horizontal variable (“run”).

• On a Velocity vs. Time graph this is the change in velocity over time, or the acceleration!

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Velocity vs. Time Graph

• Another Relationship: The area under the line on a Velocity vs. Time graph is equal to the distance traveled.

• Describe the motion of an object with a Velocity vs. Time graph shown to the right. What is the acceleration? What is the average velocity? What is the distance traveled?

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a = 4 m/s2

vavg = 20 m/s d = 200 m

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d

d

d

v

v

v

a

a

a

t t t

t t t

t t t

Summary: 1. On a distance – time graph, the

slope is the velocity. 2. On a velocity – time graph, the

slope is the acceleration. 3. On a velocity – time graph, the

area under the curve is the distance traveled.

We can consider three examples: 1. No motion, therefore no velocity

and no acceleration. 2. Uniform motion with constant

velocity and no acceleration. 3. Uniformly accelerated motion

with a changing velocity and some no-zero acceleration.

Putting it all together! Free Fall Example

The equations and the graphs should give you the same results!

Describe what happens each second at a time!

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0 5 20 45 80 125

Chapter 2 Review

1) Asteroids have been moving though space for billions of years. What keeps them moving?

2) Why do you lurch forward in a bus that suddenly slows? Why do you lurch backward when it picks up speed? What law applies here?

3) Your other friend says that bureaucratic organizations have a lot of inertia. Is this akin to Newton’s first law of inertia?

4) What kind of speed is registered by an automobile speedometer—average speed or instantaneous speed?

5) Light travels in a straight line at a constant speed of 300,000,000 m/s. What is the acceleration of light?

6) Correct your friend who says, "The race car rounded the curve at a constant velocity of 100 km/h.“

7) A basketball player's hang time would be considerably greater on the Moon. Why?

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