chapter 5 lecture conceptual integrated science second edition © 2013 pearson education, inc....

Chapter 5 Lecture

ConceptualIntegrated Science

Second Edition

© 2013 Pearson Education, Inc.

Gravity


This lecture will help you understand:

• The Legend of the Falling Apple• The Fact of the Falling Moon• Newton's Law of Universal Gravitation• Gravity and Distance: The Inverse-Square Law• The Universal Gravitational Constant, G• Weight and Weightlessness• Center of Gravity• Gravity Can Be a Centripetal Force• Projectile Motion• Projectile Altitude and Range• The Effect of Air Drag on Projectiles• Fast-Moving Projectiles—Satellites• Elliptical Orbits


The Legend of the Falling Apple

• According to legend, while Isaac Newton was sitting under an apple tree pondering the nature of forces, an apple fell and possibly struck his head. He reasoned that the Moon is falling toward the Earth for the same reason the apple falls—both are pulled by Earth's gravity.


The Fact of the Falling Moon

• In ancient times, Aristotle and others believed that stars, planets, and the Moon moved in divine circles, free from forces of Earth.


The Fact of the Falling Moon

• The Moon falls around the Earth in the sense that it falls beneath the straight line it would follow if no force acted on it.

• The Moon maintains a tangential velocity, which ensures a nearly circular motion around and around the Earth rather than into it. This path is similar to the paths of planets around the Sun.


F = Gm1 m2

d 2

Newton's Law of Universal Gravitation

• Every body in the universe attracts every other body with a mutually attracting force. For two bodies, this force is directly proportional to the product of their masses and inversely proportional to the square of the distance separating them:



• Newton discovered that gravity is universal.

• Every mass pulls on every other mass.


Newton's Law of Universal GravitationCHECK YOUR NEIGHBOR Newton's most celebrated synthesis is of

A. earthly and heavenly laws.

B. weight on Earth and weightlessness in outer space.

C. masses and distances.

D. the paths of tossed rocks and the paths of satellites.

Explain your answer to your neighbor.


Newton's Law of Universal GravitationCHECK YOUR ANSWERNewton's most celebrated synthesis is of

A. earthly and heavenly laws.

B. weight on Earth and weightlessness in outer space.

C. masses and distances.

D. the paths of tossed rocks and the paths of satellites.

Comment:

This synthesis provided hope that other natural

phenomena also followed universal laws, and it ushered

in the Age of Enlightenment.


F = Gm1 m2

d 2


• The greater m1 and m2 the greater the

force of attraction between them

• The greater the distance of separation d, the weaker is the force of attraction—weaker as the inverse square of the distance between their centers.


• The inverse-square law relates the intensity of an effect to the inverse square of the distance from the cause:

• The greater the distance from Earth, the less the gravitational force on an object.

• No matter how great the distance, gravity approaches, but never reaches, zero.

Intensity 1

distance2

Gravity and Distance: The Inverse-Square Law


Gravity and Distance:The Inverse-Square LawCHECK YOUR NEIGHBOR

The force of gravity between two planets depends on their

A. masses and distance apart.

B. planetary atmospheres.

C. rotational motions.

D. all of the above



The force of gravity between two planets depends on their

A. masses and distance apart.

B. planetary atmospheres.

C. rotational motions.

D. all of the aboveExplanation:

The equation for gravitational force cites only masses

and distances as variables. Rotation and atmospheres are irrelevant.

F = Gm1 m2

d 2

Gravity and Distance:The Inverse-Square LawCHECK YOUR ANSWER


Gravity and Distance:The Inverse-Square LawCHECK YOUR NEIGHBOR If the masses of two planets are each somehow

doubled, the force of gravity between them

A. doubles.

B. quadruples.

C. reduces by half.

D. reduces by one quarter.



Gravity and Distance:The Inverse-Square LawCHECK YOUR ANSWERIf the masses of two planets are each somehow

doubled, the force of gravity between them

A. doubles.

B. quadruples.

C. reduces by half.


Explanation:

Both masses double. Then double double = quadruple.


Gravity and Distance:The Inverse-Square LawCHECK YOUR NEIGHBOR If the mass of one planet is somehow doubled, the force of

gravity between it and a neighboring planet

A. doubles.

B. quadruples.

C. reduces by half.




If the mass of one planet is somehow doubled, the force of

gravity between it and a neighboring planet

A. doubles.

B. quadruples.

C. reduces by half.

D. reduces by one quarter.Explanation:

Let the equation guide your thinking:

Note that if one mass doubles, the force between them doubles.

F = Gm1 m2

d 2

Gravity and Distance:The Inverse-Square LawCHECK YOUR ANSWER


The Universal Gravitational Constant, G

• G is the proportionality constant in Newton's law of gravitation.

• G has the same magnitude as the gravitational force between two 1-kg masses that are 1

meter apart:

6.67 10–11 N

So, G = 6.67 10–11 N m2/kg2.

F = 6.67 10–11 N m2/kg2(m1 m2)/d2


The Universal Gravitational Constant, GCHECK YOUR NEIGHBORThe universal gravitational constant, G, which links force to

mass and distance, is similar to the familiar constant

A. .

B. g.

C. acceleration due to gravity.

D. speed of uniform motion.



The Universal Gravitational Constant, GCHECK YOUR ANSWER The universal gravitational constant, G, which links force to

mass and distance, is similar to the familiar constant

A. .

B. g.

C. acceleration due to gravity.

D. speed of uniform motion.

Explanation:

Just as relates the circumference of a circle to its

diameter, G relates force to mass and distance.


Weight and Weightlessness

• Weight is the force exerted against a supporting floor or weighing scale.

• Weightlessness is a condition in which a support force is lacking—free fall, for example.


Weight and Weightlessness

• Example of weightlessness: – An astronaut in orbit is

weightless because he or she is not supported by anything. The body responds as if gravity forces were absent, and this gives the sensation of weightlessness.


Weight and WeightlessnessCHECK YOUR NEIGHBOR

When you are in an elevator that is accelerating

upward, your weight reading on a scale is

A. greater.

B. less.

C. zero.

D. the normal weight.



Weight and WeightlessnessCHECK YOUR ANSWERWhen you are in an elevator that is accelerating upward, your weight reading on a scale is

A. greater.B. less. C. zero.D. the normal weight.

Explanation:The support force pressing on you is greater, soyou weigh more.


Weight and WeightlessnessCHECK YOUR NEIGHBORWhen you are in an elevator that is accelerating downward,

your weight reading is

A. greater.

B. less.

C. zero.




Weight and WeightlessnessCHECK YOUR ANSWER When you are in an elevator that is accelerating downward, your weight reading is

A. greater.B. less. C. zero.D. the normal weight.

Explanation:The support force pressing on you is less, so you weigh less. Question: Would you weigh less in an elevator that is moving downward at constant velocity?


Weight and WeightlessnessCHECK YOUR NEIGHBORWhen you are in an elevator and the elevator cable breaks,

the elevator falls freely and your weight reading is

A. greater.

B. less.

C. zero.




Weight and WeightlessnessCHECK YOUR ANSWERWhen you are in an elevator and the elevator cable breaks, the elevator falls freely and your weight reading is

A. greater.B. less.C. zero.D. the normal weight.

Explanation:There is still a downward gravitational force acting on you,but gravity is not felt as weight because there is no supportforce, so your weight is zero.


Weight and WeightlessnessCHECK YOUR NEIGHBORIf you weigh yourself in an elevator, you'll weigh more when

the elevator

A. moves upward.

B. moves downward.

C. accelerates upward.

D. all of the above



Weight and WeightlessnessCHECK YOUR ANSWER If you weigh yourself in an elevator, you'll weigh more whenthe elevator

A. moves upward.B. moves downward. C. accelerates upward.D. all of the above

Explanation:The support provided by the floor of an elevator is the samewhether the elevator is at rest or moving at constant velocity.Only accelerated motion affects weight.


Center of Gravity

• The center of gravity is the point located at an object's average position of weight.


Center of Gravity

• The position of object's center of gravity relative to a base of support determines the object's stability.– Rule for stability:

• If the CG of an object is above or within the area of support, the object is stable.

• If the CG of an object extends outside the area of support, the object is unstable—and it will topple.

Example: The Leaning Tower of Pisa lies above its base, soit doesn't topple.


Center of GravityCHECK YOUR NEIGHBOR

Most women's CG is

A. slightly higher than men's CG.

B. slightly lower than men's CG.

C. equal to that of men.

D. can't be determined



Center of GravityCHECK YOUR ANSWER

Most women's CG is

A. slightly higher than men's CG.

B. slightly lower than men's CG.

C. equal to that of men.

D. can't be determined

Explanation:Most women, but not all, tend to be slightly largerin the pelvis and smaller in the shoulders.


Gravity Can Be a Centripetal Force

• A centripetal force is any force that causes an object to follow a circular path.

Examples: • The Sun pulls its planets in a nearly circular path.• It is possible to whirl an empty tin can in a circular

path at the end of a string. To keep the can revolving over your head in a circular path, you must keep pulling inward on the string.


Projectile Motion

• A projectile is any object that moves through the air or through space under the influence of gravity.

• Example of the curved path of a projectile (parabola): – A stone thrown horizontally curves downward

due to gravity.


Projectile Motion

• A projectile curves as a result of two motions:– Constant motion

horizontally– Accelerated motion

vertically


Projectile MotionCHECK YOUR NEIGHBORThe velocity of a typical projectile can be represented by

horizontal and vertical components. Assuming negligible air

resistance, the horizontal component along the path of the

projectile

A. increases.

B. decreases.

C. remains the same.

D. There is not enough information.



Projectile MotionCHECK YOUR ANSWER The velocity of a typical projectile can be represented by horizontal and vertical components. Assuming negligible air resistance, the horizontal component along the path of the projectile

A. increases.B. decreases. C. remains the same.D. There is not enough information.

Explanation:Because there is no force horizontally, there is nohorizontal acceleration.


Projectile MotionCHECK YOUR NEIGHBOR

When no air resistance acts on a fast-moving

baseball, its acceleration is

A. downward, g.

B. due to a combination of constant horizontal motion and accelerated downward motion.

C. opposite to the force of gravity.

D. centripetal.



Projectile MotionCHECK YOUR ANSWER

When no air resistance acts on a fast-moving

baseball, its acceleration is

A. downward, g.

B. due to a combination of constant horizontal motion and accelerated downward motion.

C. opposite to the force of gravity.

D. centripetal.


Projectile Altitude and Range

• For equal launching speeds, the same range results from two different projection angles—apair that add up to 90.

Example:The same range occurs for a 75 launch and a 15 launch of the same initial speed.


Projectile Altitude and RangeCHECK YOUR NEIGHBOR

A ball tossed at an angle of 30 with the horizontal

will go as far downrange as one tossed at the

same speed at an angle of

A. 45.B. 60. C. 75.D. none of the above



Projectile Altitude and RangeCHECK YOUR ANSWER A ball tossed at an angle of 30 with the horizontal will go as

far downrange as one tossed at the same speed at an angle of

A. 45.B. 60. C. 75.D. none of the above

Explanation:Same initial-speed projectiles have the same range when their launching angles add up to 90. Why this is true involves a bit of trigonometry—which, in the interest of time, we'll not pursue here.


The Effect of Air Drag on Projectiles

• With air resistance, both range and altitude are decreased.

• Without air resistance, the speed lost going up is the same as the speed gained coming down.


Fast-Moving Projectiles—Satellites

• A satellite is any projectile moving fast enough to fall continuously around the Earth.

• To become an Earth satellite, the projectile's horizontal velocity must be great enough for its trajectory to match Earth's curvature.


Fast-Moving Projectiles—Satellites

• The Earth's curvature drops a vertical distance of 5 meters for each 8000 m tangent to the surface. So, to orbit Earth, a projectile must travel 8000 m in the time it takes to fall 5 m.


Fast-Moving Projectiles—SatellitesCHECK YOUR NEIGHBORWhen you toss a projectile sideways, it curves as it falls. It

will be an Earth satellite if the curve it makes

A. matches the curved surface of planet Earth.

B. results in a straight line.

C. spirals out indefinitely.

D. none of the above



Fast-Moving Projectiles—SatellitesCHECK YOUR ANSWERWhen you toss a projectile sideways, it curves as it falls. It

will be an Earth satellite if the curve it makes

A. matches the curved surface of planet Earth.

B. results in a straight line.

C. spirals out indefinitely.

D. none of the above

Explanation:

For an 8-km tangent, Earth curves downward 5 m. So, a

projectile traveling horizontally at 8 km/s will fall 5 m in that

time and follow the curve of the Earth.


Fast-Moving Projectiles—SatellitesCHECK YOUR NEIGHBOR

When a satellite travels at constant speed, the

shape of its path is

A. a circle.

B. an ellipse.

C. an oval that is almost elliptical.

D. a circle with a square corner, as seen throughout your book.



Fast-Moving Projectiles—SatellitesCHECK YOUR ANSWER

When a satellite travels at constant speed, the

shape of its path is

A. a circle.

B. an ellipse.

C. an oval that is almost elliptical.

D. a circle with a square corner, as seen throughout your book.


Elliptical Orbits

• Ellipse• The oval path followed by a satellite

• The closed path taken by a point that moves in such a way that the sum of its distances from two fixed points (called foci) is constant


Elliptical Orbits

• The speed of a satellite in an elliptical orbit varies. – Near Earth it initially starts greater than 8 km/s and

overshoots a circular orbit and travels away from Earth. Gravity slows it down until it no longer moves away from Earth. Then it falls toward Earth, gaining the speed it lost in receding. It follows the same oval-shaped path in a repetitious cycle.


Elliptical OrbitsCHECK YOUR NEIGHBOR

The speed of a satellite in an elliptical orbit

A. varies.

B. remains constant.

C. acts at right angles to its motion.

D. all of the above



Elliptical OrbitsCHECK YOUR ANSWER

The speed of a satellite in an elliptical orbit

A. varies.

B. remains constant.

C. acts at right angles to its motion.

D. all of the above


Elliptical Orbits

• The escape speed is the speed that a projectile, space probe, or similar object must reach in order to escape the gravitational influence of the Earth or of another celestial body to which it is attracted.


Elliptical Orbits

• The escape speed of a body is the initial speed given by an initial thrust, after which there is no force to assist motion.

• From Earth's surface, the escape speed is11.2 km/s.


Elliptical OrbitsCHECK YOUR NEIGHBOR

When a projectile achieves escape speed from

Earth, it

A. forever leaves Earth's gravitational field.

B. outruns the influence of Earth's gravity but is never beyond it.

C. comes to an eventual stop, returning to Earth at some future time.

D. all of the above



Elliptical OrbitsCHECK YOUR ANSWER

When a projectile achieves escape speed from

Earth, it

A. forever leaves Earth's gravitational field.

B. outruns the influence of Earth's gravity but is never beyond it.

C. comes to an eventual stop, returning to Earth at some future time.

D. all of the above

chapter 5 lecture conceptual integrated science second edition © 2013 pearson education, inc....

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