Lesson 2Lesson 2

NewtonNewton’’s Second Laws Second Law

Newton’s Second Law of Motion The acceleration of an object is directly

proportional to the net force acting on it and inversely proportional to its mass.

F = ma

GravityGravity Gravity

force of attraction between any two objects in the universe

increases as... mass increases distance decreases

If the mass of either of the objects increases, the gravitational force between them increases

If the objects are closer together, the gravitational force between them increases

GravityGravity

Who experiences more gravity - the Who experiences more gravity - the astronaut or the politician?astronaut or the politician?

less distance

more mass

Which exerts more gravity - theWhich exerts more gravity - the

Earth or the moon?Earth or the moon?

GravityGravity• Gravity is one of the Gravity is one of the fourfour basic forces. basic forces.

The other basic forces are the The other basic forces are the electromagneticelectromagnetic force, the strong force, the strong nuclearnuclear force, and the force, and the weakweak nuclear force. nuclear force.

Isaac Newton formulated the law of Isaac Newton formulated the law of universal gravitation, which he published universal gravitation, which he published in 1687.in 1687.

The further from earth you travel the less The further from earth you travel the less gravitational force is on you. gravitational force is on you.

The Range of Gravity The Range of Gravity According to the law of universal According to the law of universal

gravitation, the gravitational force between gravitation, the gravitational force between two masses decreases rapidly as the two masses decreases rapidly as the distancedistance between the masses increases. between the masses increases.

No matter how far apart two objects are, No matter how far apart two objects are, the the gravitationalgravitational force between them force between them never completely goes to zero. never completely goes to zero.

Because the gravitational force between Because the gravitational force between two objects never disappears, gravity is two objects never disappears, gravity is called a long-range called a long-range forceforce. .

EarthEarth’’s Gravitational s Gravitational Acceleration Acceleration

When all forces except gravity acting When all forces except gravity acting on a falling object can be ignored, the on a falling object can be ignored, the object is said to be in object is said to be in free fallfree fall..

Close to EarthClose to Earth’’s surface, the s surface, the acceleration of a falling object in free acceleration of a falling object in free fall is about fall is about 9.8 m/s9.8 m/s22..

This acceleration is given the symbol This acceleration is given the symbol gg and is sometimes called the and is sometimes called the acceleration of acceleration of gravitygravity. .

EarthEarth’’s Gravitational s Gravitational Acceleration Acceleration

Close to EarthClose to Earth’’s surface, the acceleration s surface, the acceleration of a falling object in free fall is about of a falling object in free fall is about 9.8 9.8 m/sm/s22..

This acceleration is given the symbol This acceleration is given the symbol gg and is sometimes called the acceleration and is sometimes called the acceleration of gravity. of gravity.

By NewtonBy Newton’’s second law of motion, the s second law of motion, the force of Earthforce of Earth’’s gravity on a falling object s gravity on a falling object is the objectis the object’’s mass times the s mass times the accelerationacceleration of gravity. of gravity.

WeightWeight

The gravitational force exerted on an The gravitational force exerted on an object is called the objectobject is called the object’’s s weightweight

Because the weight of an object on Because the weight of an object on Earth is Earth is equalequal to the force of Earth to the force of Earth’’s s gravity on the object, weight can be gravity on the object, weight can be calculated from this equation: calculated from this equation:

GravityGravity WeightWeight

the force of gravity on an objectthe force of gravity on an object

MASSalways the same

(kg)

WEIGHTWEIGHTdepends on gravitydepends on gravity

(N)(N)

W = mgW:weight (N)m: mass (kg)g: acceleration

due to gravity (m/s2)

GravityGravity Would you weigh more on Earth or Would you weigh more on Earth or

Jupiter?Jupiter?

greater gravitygreater gravity

greater weightgreater weight

greater massgreater mass

Jupiter becauseJupiter because......

Weight and Mass Weight and Mass

Weight and mass are Weight and mass are notnot the same the same WeightWeight is a force and mass is a is a force and mass is a

measure of the amount of matter an measure of the amount of matter an object contains. object contains.

Weight and mass are Weight and mass are relatedrelated. Weight . Weight increases as mass increases. increases as mass increases.

The weight of an object usually is the The weight of an object usually is the gravitationalgravitational force between the object force between the object and Earth.and Earth.

GravityGravity• The weight of an object can change, The weight of an object can change,

dependingdepending on the gravitational force on the gravitational force on the object.on the object.

• The table shows how various weights The table shows how various weights on Earth would be different on the on Earth would be different on the Moon and some of the planets.Moon and some of the planets.

Weightlessness and Free Weightlessness and Free FallFall

YouYou’’ve probably seen pictures of ve probably seen pictures of astronauts and equipment floating astronauts and equipment floating inside the space shuttle. inside the space shuttle.

They are said to be experiencing the They are said to be experiencing the sensation of weightlessness. sensation of weightlessness.

Floating in SpaceFloating in Space

The dial on the scale shows the The dial on the scale shows the upward force exerted by the scale, upward force exerted by the scale, which is your weight.which is your weight.

Now suppose you stand on the scale Now suppose you stand on the scale in an elevator that is falling.in an elevator that is falling.

Floating in SpaceFloating in Space

If you and the scale were in free fall, If you and the scale were in free fall, then you no longer would then you no longer would pushpush down down on the scale at all.on the scale at all.

The scale dial would say you have The scale dial would say you have zerozero weight, even though the force of weight, even though the force of gravity on you hasngravity on you hasn’’t changed. t changed.

Free-FallFree-Fall

Free-FallFree-Fall when an object is influenced only by the force when an object is influenced only by the force

of gravityof gravity

WeightlessnessWeightlessness sensation produced when an object sensation produced when an object andand its its

surroundings are in free-fallsurroundings are in free-fall object is object is notnot weightless! weightless!

CUP DEMO

Floating in SpaceFloating in Space

A space shuttle in orbit is in free fall, but A space shuttle in orbit is in free fall, but it is falling around Earth, rather than it is falling around Earth, rather than straight straight downwarddownward. .

Everything in the orbiting space shuttle is Everything in the orbiting space shuttle is fallingfalling around Earth at the same rate, in around Earth at the same rate, in the same way you and the scale were the same way you and the scale were falling in the elevatorfalling in the elevator

Objects in the shuttle seem to be floating Objects in the shuttle seem to be floating because they are all falling with the same because they are all falling with the same accelerationacceleration. .

Projectile MotionProjectile Motion

If youIf you’’ve tossed a ball to someone, ve tossed a ball to someone, youyou’’ve probably noticed that thrown ve probably noticed that thrown objects donobjects don’’t always travel in straight t always travel in straight lines. They curve lines. They curve downwarddownward. .

EarthEarth’’s s gravitygravity causes projectiles to causes projectiles to follow a curved path. follow a curved path.

Horizontal and Vertical Horizontal and Vertical Motions Motions

When you throw a ball, the force When you throw a ball, the force exerted by your hand exerted by your hand pushespushes the ball the ball forward.forward.

This force gives the ball horizontal This force gives the ball horizontal motionmotion..

No force accelerates it forward, so its No force accelerates it forward, so its horizontal horizontal velocityvelocity is constant, if you is constant, if you ignore air resistance. ignore air resistance.

Horizontal and Vertical Horizontal and Vertical MotionsMotions

However, when you let go of the ball, However, when you let go of the ball, gravitygravity can pull it downward, giving it can pull it downward, giving it vertical motion.vertical motion.

The ball has constant horizontal The ball has constant horizontal velocity but increasing velocity but increasing verticalvertical velocity velocity

Gravity exerts an Gravity exerts an unbalancedunbalanced force on force on the ball, changing the direction of its the ball, changing the direction of its path from only forward to forward and path from only forward to forward and downward. downward.

Horizontal and Vertical Horizontal and Vertical MotionsMotions

The result of these two motions is The result of these two motions is that the ball that the ball appearsappears to travel in a to travel in a curvecurve. .

If you were to throw a ball as hard as If you were to throw a ball as hard as you could from shoulder height in a you could from shoulder height in a perfectly horizontal direction, would perfectly horizontal direction, would it take longer to reach the ground it take longer to reach the ground than if you dropped a ball from the than if you dropped a ball from the same height? same height?

Horizontal and Vertical Horizontal and Vertical MotionsMotions

Surprisingly, it Surprisingly, it wouldnwouldn’’tt. . Both balls travel the Both balls travel the samesame vertical vertical

distance in the same amount of time.distance in the same amount of time.

Centripetal ForceCentripetal Force

When a ball enters a curve, even if its When a ball enters a curve, even if its speed does not change, it is speed does not change, it is acceleratingaccelerating because its direction is changing. because its direction is changing.

When a ball goes around a curve, the When a ball goes around a curve, the change in the direction of the velocity is change in the direction of the velocity is toward the center of the curve.toward the center of the curve.

Acceleration toward the center of a Acceleration toward the center of a curved or circular path is called curved or circular path is called centripetal accelerationcentripetal acceleration..

Centripetal ForceCentripetal Force

According to the second law of According to the second law of motion, when a ball has centripetal motion, when a ball has centripetal acceleration, the direction of the net acceleration, the direction of the net force on the ball also must be toward force on the ball also must be toward the the centercenter of the curved path. of the curved path.

The net force exerted toward the The net force exerted toward the center of a curved path is called a center of a curved path is called a centripetal forcecentripetal force. .

Centripetal Force and Centripetal Force and TractionTraction

When a car rounds a When a car rounds a curvecurve on a highway, on a highway, a centripetal force must be acting on the a centripetal force must be acting on the car to keep it moving in a curved path.car to keep it moving in a curved path.

This centripetal force is the frictional This centripetal force is the frictional force, or the force, or the tractiontraction, between the tires , between the tires and the road surface. and the road surface.

Anything that moves in a circle is doing Anything that moves in a circle is doing so because a so because a centripetalcentripetal force is force is accelerating it toward the center. accelerating it toward the center.

Gravity Can Be a Gravity Can Be a Centripetal Force Centripetal Force

Imagine Imagine whirlingwhirling an object tied to a an object tied to a string above your head.string above your head.

The string exerts a centripetal force The string exerts a centripetal force on the object that keeps it moving in on the object that keeps it moving in a a circularcircular path. path.

In the same way, EarthIn the same way, Earth’’s gravity s gravity exerts a centripetal force on the exerts a centripetal force on the Moon that keeps it moving in a Moon that keeps it moving in a nearly circular orbit. nearly circular orbit.

ConcepTestConcepTest Is the following statement true or false?Is the following statement true or false?

An astronaut has less mass on the moon since An astronaut has less mass on the moon since the moon exerts a weaker gravitational force.the moon exerts a weaker gravitational force.

False! Mass does not depend on gravity, weight does. The astronaut has less weight on the moon.

ConcepTestConcepTest

Describe the path of a marble as it leaves Describe the path of a marble as it leaves the spiral tube shown below.the spiral tube shown below.

It will travel in a straight line since the tube is no longer exerting a net force on it.

ConcepTestConcepTest A moving truck launches a ball vertically (relative A moving truck launches a ball vertically (relative

to the truck). If the truck maintains a constant to the truck). If the truck maintains a constant horizontal velocity after the launch, where will horizontal velocity after the launch, where will the ball land (ignore air resistance)?the ball land (ignore air resistance)?

A) In front of the truck A) In front of the truck

B) Behind the truck B) Behind the truck

C) In the truckC) In the truck

C) In the truck. The horizontal velocity of the ball remains constant and is unaffected by its vertical motion.

Animation from “Multimedia Physics Studios.”

ConcepTestConcepTest

TRUE or FALSE:TRUE or FALSE:

An astronaut on the Space Shuttle feels An astronaut on the Space Shuttle feels weightless because there is no gravity in weightless because there is no gravity in space.space.

FALSE! There is gravity which is causing the Shuttle to free-fall towards the Earth. She feels weightless because she’s free-falling at the same rate.