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Forces, Momentum, & Gravity

(Chapter 3)

Force and Motion – Cause and Effect

• In chapter 2 we studied motion but not its cause.

• In this chapter we will look at both force and motion – the cause and effect.

• We will consider Newton’s: – Newton’s three laws of motion

– Newton’s law of universal gravitation

– Buoyancy and momentum

Intro

Student Learning Objectives • Recall and apply each of Newton’s Laws

• Relate momentum to impact force

• Use conservation of momentum to analyze motion

• Describe gravity and its applications.

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Sir Isaac Newton (1642 – 1727)

• Only 25 when he formulated most of his discoveries in math and physics

• His book Mathematical Principles of Natural Philosophy is considered to be the most important publication in the history of Physics.

Intro

What is a force & when are forces balanced?

A force is the amount of push or pull on an object.

Forces can cause a change in motion; a net force results in acceleration.

An object in mechanical equilibrium maintains its motion. There is no change.

Fnet = 0

Forces are balanced

Fnet = ∑ F

Balanced (equal) forces, therefore no motion.

Section 3.1

Equal in magnitude but in opposite directions.

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Unbalanced forces result in motion

Section 3.1

Net force to the right

Practice 1) A 150 lb person is standing still on the floor. What is the net

force?

2) If a car engine provides 700 Newtons of push, and there is 200 Newtons of opposing friction, what is the net force on the car?

3) When the car engine continues to provide 700 Newtons of push, but the friction force is increased to 700 Newtons, what is the net force on the car? Would this cause the car to stop?

4) Is a car with a constant velocity of 30 mph in mechanical equilibrium? Why must you keep pressure on the accelerator?

What are Newton’s Laws of Motion & how do they apply?

All objects have the same motion within a specific reference frame.

Newton’s 1st Law of Motion: Inertia

An object will remain at rest or maintain a constant velocity unless an unbalanced force causes the object’s motion to change.

Inertia is the tendency of an object to maintain its motion.

Quick stops Cornering Something sliding across your dash as you turn The tablecloth trick

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A spacecraft keeps going because no forces act to stop it

Photo Source: Copyright © Bobby H. Bammel. All rights reserved.

Section 3.2

A large rock in Yellowstone N.P. stays put until a large enough force acts on it.

Photo Source: Copyright © Bobby H. Bammel. All rights reserved.

Section 3.2

http://www.physicsclassroom.com/mmedia/newtlaws/cci.cfm

https://www.youtube.com/watch?v=d7iYZPp2zYY

Mass Inertia depends on mass.

Mass is the amount of material contained in an object.

Mass is a fundamental quantity.

more mass more inertia harder to change motion

Empty 747 Jet 160,000 kg

Average Man 73 kg

5¢ coin 0.0052 kg

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Mass and Inertia

The large man has more inertia – more force is necessary to start him swinging and also to stop him – due to his greater inertia

Section 3.2

Mass and Inertia

Quickly pull the paper and the stack of quarters tend to stay in place due to inertia.

Section 3.2

Practice: Mass is often defined in elementary school as “the amount of space an object takes up”. Why is this not correct?

Newton’s 2nd Law of Motion: F = ma

An unbalanced force acting on a mass gives the mass an acceleration in the same direction as the unbalanced force.

Example: Soccer ball

F = ma

http://www.grc.nasa.gov/WWW/k-12/airplane/socforce.html

https://www.youtube.com/watch?v=8HgNS1yqaB0

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Force, Mass, Acceleration a) Original situation

a F m

b) If we double the force we double the acceleration.

c) If we double the mass we half the acceleration.

Section 3.3

When an object is in motion, friction is always in the opposite direction of the motion.

Big Box

Ff

Motion

Practice 1) If the force on a 5 kg mass is tripled, what will happen to the rate

of acceleration?

2) A 2000 kg car engine provides 9800 N of push southward. The opposing frictional force is 1200 N. What is the average acceleration?

Weight is a force; it is the gravitational force acting on a mass.

1 kg of mass weighs 9.8 Newtons or 2.2 pounds on Earth.

W = mg

Practice 1) Does weight depend on

volume?

2) Would 1 kg of mass weigh 2.2 pounds on the Moon?

3) If you were instantly transportedto Mars, what would change?

a. Mass? b. Weight? c. Inertia?

4) What would a person weigh on Mars if the person weighs150 lb(667 N) on Earth? The acceleration due to gravity on Mars is 3.72 m/s2.

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Vectors

Forces are vectors, and vector addition is the addition of both the size and direction of each quantity.

The resultant vector shows the result of two or more vectors acting simultaneously.

http://www.physicsclassroom.com/mmedia/vectors/rb.cfm

http://www.physicsclassroom.com/mmedia/vectors/plane.cfm

Practice

An airplane’s speedometer reads 500 mph North. What is the net velocity of the airplane in each case?

a) Wind is blowing North at 50 mph.

b) Wind is blowing South at 50 mph.

c) Wind is blowing East at 50 mph.

Newton’s 3rd Law of Motion: Action-Reaction

When two objects interact, they create equal and opposite forces on each other.

To every action force there is an equal (in magnitude) and opposite (in direction) reaction force when two objects are in contact.

Examples: Pushing on a wall, Bat & Ball, Rockets

F1 = − F2

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Newton's Laws in Action

• Friction on the tires provides necessary centripetal acceleration.

• Passengers continue straight ahead in original direction and as car turns the door comes toward passenger – 1st Law

• As car turns you push against door and the door equally pushes against you – 3rd Law

Section 3.4

http://www.wimp.com/golfball/

http://www.cnn.com/videos/us/2015/02/11/sot-spacex-rocket-launch.nasa-tv

Practice If I give the chair a good push, it goes from rest to having a velocity, and then stops. How do each of Newton’s laws apply to this system?

What is momentum?

Linear momentum is the combination of mass (inertia) and velocity.

The greater the momentum, the harder it is to stop an object!

p = mv

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Momentum

• If we have a system of masses, the linear momentum is the sum of all individual momentum vectors.

• Pf = Pi (final = initial)

• P = p1 + p2 + p3 + … (sum of the individual momentum vectors)

Section 3.7

Law of Conservation of Linear Momentum

• Law of Conservation of Linear Momentum -the total linear momentum of an isolated system remains the same if there is no external, unbalanced force acting on the system

• Linear Momentum is ‘conserved’ as long as there are no external unbalance forces. – It does not change with time.

Section 3.7

Conservation of Linear Momentum

• Pi = Pf = 0 (for man and boat) • When the man jumps out of the boat he has momentum in one

direction and, therefore, so does the boat. • Their momentums must cancel out! (= 0)

Section 3.7

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Applying the Conservation of Linear Momentum

• Two masses at rest on a frictionless surface. When the string (weightless) is burned the two masses fly apart due to the release of the compressed (internal) spring (v1 = 1.8 m/s).

Section 3.7

Applying the Conservation of Linear Momentum

• Two masses at rest on a frictionless surface. When the string (weightless) is burned the two masses fly apart due to the release of the compressed (internal) spring (v1 = 1.8 m/s).

GIVEN: •Pf = Pi = 0 • m1 = 1.0 kg • Pf = p1 + p2 = 0 • m2 = 2.0 kg • p1 = -p2• v1 = 1.8 m/s, v2 = ?

•m1v1 = -m2v2

Section 3.7

Applying the Conservation of Linear Momentum

m1v1 = -m2v2

v2 = - m1v1 = - (1.0 kg) (1.8 m/s) = -0.90 m/s m2 2.0 kg

Section 3.7

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Jet Propulsion

• Jet Propulsion can be explained in terms of both Newton’s 3rd Law & Linear Momentum

• p1 = -p2 m1v1 = -m2v2

• The exhaust gas molecules have small m and large v.

• The rocket has large m and smaller v.

• BUT m1v1 = -m2v2 (momentum is conserved)

Section 3.7

Practice

1) What is an example of a moving object that could have a large momentum because it has a large mass?

2) What is an example of a small object that could have a large momentum because it has a large velocity?

3) Which has the most momentum?

a) 10,000 lb (4535 kg) 18-wheeler parked at the curb

b) 300 lb (136 kg) football player running 10 mph (4.46 m/s)

c) 150 lb (68 kg) sprinter running 22 mph (9.83 m/s)

d) 1200 kg car moving at 1 m/s

Torque

• Torque – the twisting effect caused by one or more forces

• As we have learned, the linear momentum of a system can be changed by the introduction of an external unbalanced force.

• Similarly, angular momentum can be changed by an external unbalanced torque.

https://www.youtube.com/watch?v=H4JUTnkiGpI

Section 3.7

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• Torque is a twisting action that produces rotational motion or a change in rotational motion.

Torque

Section 3.7

Torque and Lever Arm

• Torque varies with the length of the lever arm. As the length of the lever arm is doubled, the torque is doubled, for a given force.

Section 3.7

Law of Conservation of Angular Momentum

• Law of Conservation of Angular Momentum -the angular momentum of an object remains constant if there is no external, unbalanced torque (a force about an axis) acting on it

• Concerns objects that go in paths around a fixed point, for example a satellite orbiting the earth

https://www.youtube.com/watch?v=RMWJ7wA09gE

Section 3.7

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• L = mvr

• L = angular momentum, m = mass, v = velocity, and r = distance to center of motion

• L1 = L2

• m1v1r1 = m2v2r2

Angular Momentum

Section 3.7

Angular Momentum - Example

• Mass (m) is constant.

• As r changes so must v. When r decreases, v must increase so that m1v1r1 = m2v2r2

Section 3.7

Angular Momentum in our Solar System

• In our solar system the planet’s orbit paths are slightly elliptical, therefore both r and v will slightly vary during a complete orbit.

Section 3.7

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Conservation of Angular Momentum Example

• A comet at its farthest point from the Sun is 900 million miles, traveling at 6000 mi/h. What is its speed at its closest point of 30 million miles away?

• EQUATION: m1v1r1 = m2v2r2

• GIVEN: v2, r2, r1, and m1v2r2• FIND: v1 = = r1

• 1.8 x 105 mi/h or 180,000 mi/h

Section 3.7

= m2(6.0 x 103 mi/h) (900 x 106 mi) 30 x 106 mi

Conservation of Angular Momentum

Rotors on large helicopters rotate in the opposite direction

Section 3.7

Conservation of Angular Momentum

• Figure Skater – she/he starts the spin with arms out at one angular velocity. Simply by pulling the arms in the skater spins faster, since the average radial distance of the mass decreases.

• m1v1r1 = m2v2r2

• m is constant; r decreases;

• Therefore v increases

Section 3.7

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Angular momentum is momentum in a circular path.

The angular momentum vector is perpendicular to the plane of the circular path.

L = mvr

L

v

http://hyperphysics.phy-astr.gsu.edu/hbase/bike.html

https://www.youtube.com/watch?v=8H98BgRzpOM

How does momentum affect the force of impact?

https://www.youtube.com/watch?v=qLp6qH1Izxw

https://www.youtube.com/watch?v=r8E5dUnLmh4

During an impact, the force of impact depends on how quickly the momentum is changed.

Examples: – Water barrels at the start of a divided highway

– Carpet vs. concrete

F = p t

Practice

1) You (75 kg) are riding in your 2000 kg car at 30 m/s (67 mph) when suddenly a squirrel runs in front of you; you swerve, and hit a tree. If the duration of the impact is 1/2 of a second, what is the impact force?

2) Two 2000 kg cars, each with a 75 kg person, are traveling toward each other with a speed of 30 m/s (67 mph); suddenly one swerves into the wrong lane and there is a head-on collision. If the duration of the impact is 1/2 of a second, what is the impact force?

3) What are some features of car design that decrease force of impact?

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How is conservation of momentum applied?

The total momentum of an isolated system remains constant.

Examples: Collisions & Ice Skaters

pf = pi Lf = Li

http://www.physicsclassroom.com/mmedia/momentum

https://www.youtube.com/watch?v=WSg28pzVXjs

https://www.youtube.com/watch?v=AQLtcEAG9v0

Practice

Always assume momentum is conserved.

1)Two cars of equal mass collide. One is traveling West at 30 m/s, the other is at rest. Then there is an inelastic collision between the two cars. If linear momentum is conserved, what is the final velocity of each car?

2) An ice skater spins 5 m/s with outstretched arms. The radius of the circular path traced by her arms is 1 meter. Then she pulls her arms in, changing the radius of the circular path to1/3 m. If angular momentum is conserved, what is her new spinning speed?

Newton’s Law of Gravitation

• Gravity is a fundamental force of nature – We do not know what causes it – We can only describe it

• Law of Universal Gravitation – Every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them

Section 3.5

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What is Newton’s description of gravity?

Newton’s Universal Law of Gravitation

Mutual force of attraction

All masses pull the same on each other!

Causes acceleration due to gravity, g = 9.81 m/s2

Fg = GMm d2

G is the universal gravitational constant G = 6.67 x 10-11 N.m2/kg2

G: is a very small quantity thought to be valid throughout the universe was measured by Cavendish 70 years after Newton’s death not equal to “g” and not a force

http://hyperphysics.phy-astr.gsu.edu/hbase/forces/isq.html

Newton’s Law of Gravitation

• The forces that attract particles together are equal and opposite

• F1 = -F2 or m1a1 = -m2a2

Section 3.5

Newton's Law of Gravitation

Gm1m2• F =

r2

• For a homogeneous sphere the gravitational force acts as if all the mass of the sphere were at its center

Section 3.5

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• Two objects with masses of 1.0 kg and 2.0 kg are 1.0 m apart. What is the magnitude of the gravitational force between the masses?

Applying Newton’s Law of Gravitation

Section 3.5

Applying Newton’s Law of Gravitation – Example

• Two objects with masses of 1.0 kg and 2.0 kg are 1.0 m apart. What is the magnitude of the gravitational force between the masses?

Gm1m2• F = r2

(1.0 m)2 (6.67 x 10-11 N-m /kg )(1.0 kg)(2.0 kg) • F =

• F = 1.3 x 10-10 N

Section 3.5

Practice

1) Would the acceleration due to gravity (9.81 m/s2) be different for anobject dropped from a high mountain top than it is at sea level?

2) If Earth had twice as much mass, would this change our weight?Would it change our mass?

3) What is the gravitational attraction between Earth and a 75 kg person standing on the surface, at sea level (ME = 6 x 1024 kg, rE = 6.4 x 106

m)? What do we normally call this?

4) How would the gravitational force change if the distance doubled?

5) Is the gravitational force zero in space?

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What are some effects of gravity?

https://www.youtube.com/watch?v=WMK36dpHIkg

The feeling of weightlessness occurs when an object and its reference frame accelerate at the same rate.

– Airplane drops

– Large, rolling “dip” in the road

– Freefall ride

If there is no support force, then objects will fall together.

https://www.youtube.com/watch?v=BV7TPvk__kE

Practice

If you were standing on a scale in the elevator that measured your weight, how would the scale reading change as the elevator

a) Accelerates up

b) Accelerates down

c) Free falls

Gravity Effects Orbits Tides

Atmospheres Changing Earth-Moon System

Changing Earth-Moon system:

Earth’s rotation is slowing (0.0015 seconds/century)

Our Moon is drifting away (3.8 cm/year)

The synchronous orbit of the Moon (same face)

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“Weightlessness” in space is the result of both the astronaut and the spacecraft ‘falling’ to Earth at the same rate

Section 3.5

Photo Source: Standard HMCO copyright line

https://www.youtube.com/watch?v=l37ofe9haMU

Practice: The Sun's tidal affects are weak compared to the Moon. Why?

What is Einstein’s description of Gravity?

Every object with mass creates a curvature of space-time.

https://www.youtube.com/watch?v=LoaOHvy5AcA

https://www.youtube.com/watch?v=JZWyAVN970c

According to Einstein, mass does not create a force, but rather a warping of space which other objects follow.

More Mass = More Curvature

Objects fall independent of their mass because they all follow the same path in curved space-time.

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