Lecture 3Lecture 3Newton’s Three Laws of MotionNewton’s Three Laws of Motion

Homework AssignmentHomework Assignment

• A few rules to remember:

– At rest or constant velocity = no change in motion

– No change in motion = no acceleration = No Net Force (ΣF= 0)

Origins of Modern AstronomyOrigins of Modern Astronomy

• Sir Isaac Newton (1642-1727)

– Formulated the laws of motion and gravitation that govern all bodies in the universe.

Newton’s First Law of MotionNewton’s First Law of Motion

• The Law of Inertia:Every object continues in a state of rest or of uniform speed in a straight line unless acted on by a nonzero force.

• Inertia: The property of objects to resist changes in motion.

The Earth in MotionThe Earth in Motion

• Nicolaus Copernicus (1473-1543):

– Proposed that the Earth revolved around the Sun from observations of the motion of planets.

– Because the concept of inertia was unknown at his time, the idea of a moving Earth was difficult to comprehend.

If the Earth moves at 30 km/s, how can the bird drop down and catch the worm?

Thanks to inertia, you can flip a coin in an airplane without having it fly into your face at 500 mph.

Newton’s Second Law of MotionNewton’s Second Law of Motion

• The acceleration produced by a net force on an object:

– is directly proportional to the net force,– is in the same direction as the net force,– and is inversely proportional to the mass of the object.

Newton’s Second Law of MotionNewton’s Second Law of Motion

Acceleration = net force / mass

a = F / m

Newton’s Second Law of MotionNewton’s Second Law of Motion

• Net Force = mass x acceleration

• F = ma

• Units: 1 N = 1 kg∙m/s2

You apply the same amount of force on two separate carts; You apply the same amount of force on two separate carts; one cart with mass of 1 kg and another with a mass of 2 kg. one cart with mass of 1 kg and another with a mass of 2 kg. Which of the following is correct?Which of the following is correct?

1. 2. 3. 4.

0% 0%0%0%

1. The acceleration of the 2 kg cart will be ½ as much as that of the 1 kg cart.

2. The acceleration of the 2 kg cart will be 2 times greater than that of the 1 kg cart.

3. The acceleration will be the same for both carts.

4. The acceleration of the 2 kg cart will be ¼ as much as that of the 1 kg cart.

A jumbo jet cruises at a constant velocity of 1000 km/h A jumbo jet cruises at a constant velocity of 1000 km/h when the thrusting force of its engines are a constant when the thrusting force of its engines are a constant 100,000 N. What is the force of air resistance on the jet?100,000 N. What is the force of air resistance on the jet?

1. 2. 3. 4.

0% 0%0%0%

1. 0 N2. 100,000 N3. 1,000 N4. There is not

enough information to answer this question.

How much force, or thrust, must a 20,000-kg jet How much force, or thrust, must a 20,000-kg jet plane develop to achieve an acceleration of 2 plane develop to achieve an acceleration of 2 m/sm/s22??

1. 2. 3. 4. 5. 6.

0% 0% 0%0%0%0%

1. 10,000 N2. 10,000 m/s2

3. 20,000 N4. 20,000 m/s2

5. 40,000 N6. 40,000 m/s2

A constant g on EarthA constant g on Earth

• Galileo was the first to measure the acceleration of objects in free fall, but could not explain why they all fall equally.

• Greater the mass = stronger gravitational pull.

A constant g on EarthA constant g on Earth

A constant g on EarthA constant g on Earth

• g (10m/s2) is independent of an object’s mass.

In a vacuum, a coin and a feather fall equally, side In a vacuum, a coin and a feather fall equally, side by side. Would it be correct to say that by side. Would it be correct to say that equal equal forcesforces of gravity of gravity act on both the coin and the act on both the coin and the feather in a vacuum?feather in a vacuum?

1. 2.

0%0%

1. Yes2. No

A constant g on EarthA constant g on Earth

WeightWeight

• Calculating Weight using Newton’s Second Law:

F = maWeight = mg

g = acceleration due to gravity on Earth

Falling Objects and Air ResistanceFalling Objects and Air Resistance

• On Earth, air-resistance must be considered for falling objects.

• As falling speed increases so does the opposing force of air-resistance.

Net force (ΣF) = Weight – Air-resistance

a = ΣF / ma = (mg - R )/ m

R = force due to Air Resistancemg = weight

Falling Objects and Air ResistanceFalling Objects and Air Resistance

• Acceleration of falling object calculated using Newton’s 2nd Law:

Terminal VelocityTerminal Velocity• Terminal velocity reached when the force of air-

resistance = the falling object’s weight.

• No net force (ΣF= 0) = no acceleration = no change in velocity

a = ΣF / m = 0

a = (mg - R )/ m = 0

Terminal VelocityTerminal Velocity

• Varies from 150 to 200 km/h for a human skydiver.

A bowling ball and a feather are dropped from the A bowling ball and a feather are dropped from the same height at the same time. Which reaches same height at the same time. Which reaches terminal velocity first?terminal velocity first?

1. 2.

0%0%

1. Bowling Ball2. Feather

A bowling ball and a feather are dropped from the same A bowling ball and a feather are dropped from the same height at the same time. Which has the greater terminal height at the same time. Which has the greater terminal velocity?velocity?

1. 2.

0%0%

1. Bowling Ball2. Feather

Terminal VelocityTerminal Velocity

• Greater force of air resistance (R) needed to cancel out the weight (mg) of heavier objects in free fall

• Greater R requires a greater velocity which requires acceleration for a longer period of time.

Effect of air-resistance on falling objectsEffect of air-resistance on falling objectsInitially velocity is 0Air-resistance is 0

Net Force = 100 NInitial Acceleration is

10m/s2

Velocity has increasedAir-resistance increases

Net Force = 60 NAcceleration is less due

to smaller net force

R = 40 NR = 0 N

Velocity continues to increaseAir-resistance increases

Net Force = 20 NAcceleration has decreased more

R = 80 N

Weight = 100 N Weight = 100 N Weight = 100 N

Velocity no longer changes(Terminal Velocity)

Air-resistance is 100 N

Net Force = 0 NAcceleration = 0 m/s2

R = 100 N

Effect of air-resistance on falling objectsEffect of air-resistance on falling objects

No net force = no acceleration = no change in velocity!

Weight = 100 N

A bowling ball and a feather are dropped from the same A bowling ball and a feather are dropped from the same height at the same time. Which would strike the ground first height at the same time. Which would strike the ground first if it were on the Moon?if it were on the Moon?

1. 2. 3.

0%0%0%

1. Bowling Ball2. Feather3. Both at the same

time

Forces and InteractionsForces and Interactions

• A force is not a thing in itself but makes up an interaction between one thing and another.

• Force Pair: two forces that are equal in magnitude and opposite in direction.

– Constitutes a single interaction.

Forces and InteractionsForces and Interactions

• You can only exert as much force on an object as it can exert back on you.

Forces and InteractionsForces and Interactions

Newton’s Third Law of MotionNewton’s Third Law of Motion

• Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

• Action force and reaction force

To every action there is always an opposed equal To every action there is always an opposed equal reaction:reaction:

Action and ReactionAction and Reaction

• Earth is pulled up by the boulder with just as much force as the boulder is pulled down by Earth.

• Forces are equal in magnitude but what about the acceleration of the two objects?

A speeding bus and an insect experience a head-on A speeding bus and an insect experience a head-on collision. The force of the bus on the insect splatters it on collision. The force of the bus on the insect splatters it on the windshield. Is the corresponding force of the insect on the windshield. Is the corresponding force of the insect on the bus greater, less, or the same?the bus greater, less, or the same?

1. 2. 3.

0%0%0%

1. Greater2. Less3. The same

What about the resulting acceleration that What about the resulting acceleration that the bug experiences?the bug experiences?

1. 2. 3.

0%0%0%

1. Greater than the acceleration of the bus.

2. Less than the acceleration of the bus.

3. The accelerations are the same.

Equal and opposite forces does not always mean equal and opposite accelerations.

Action and ReactionAction and Reaction

F = 10,000 N

Cannonball = 20 kgCannon = 500 kg

F = 10,000 N

a = 500 m/s2a = 20 m/s2

Chuck Norris delivers a roundhouse kick with a force of Chuck Norris delivers a roundhouse kick with a force of 8,000 N to an opponent. Assuming that the laws of physics 8,000 N to an opponent. Assuming that the laws of physics apply to Chuck Norris, how much force is exerted back on apply to Chuck Norris, how much force is exerted back on his foot?his foot?

1. 2. 3. 4. 5.

0% 0%0%0%0%

1. Less than 8,000 N2. More than 8,000 N3. 8,000 N4. There’s not enough

information to answer this question.

5. I’m too intimidated by Chuck Norris to answer this question

Assume that Chuck Norris has a mass of 100 kg and his Assume that Chuck Norris has a mass of 100 kg and his opponent has a mass of 80 kg. The force exerted on each opponent has a mass of 80 kg. The force exerted on each was 8,000 N in the previous question. What is the was 8,000 N in the previous question. What is the acceleration of his opponent during impact?acceleration of his opponent during impact?

1. 2. 3. 4. 5.

0% 0%0%0%0%

1. 8,000 m/s2

2. 20 m/s2

3. 100 m/s2

4. 80 m/s2

5. 640,000 m/s2

Defining a SystemDefining a System

• If action and reaction forces on an object are equal and opposite, then how can an object accelerate?

– An acceleration of a system is only possible if a force external to the system is involved.

FlightFlight• Lift: an upward reaction force that allows for

flight.

• When the force of lift exceeds an object’s weight it will accelerate upward.

– A helicopter’s whirling blades are shaped to force air downward and the air forces the blades up.

A bird’s wing pushes down on the air and the air pushes back on the wing.