PHYS 1301 - Ch. 3 (LearnSmart & Connect).

A planet's orbit around the Sun is a curved path. This implies that

a force acts on the planets. (if gravity weren't exerting a force, the path would be a straight line.)

Newton's work added ___________ to Kepler's laws.

a physical reason.

Match the variables and constants from the modified form of Kepler's third law to their correct units.

d - meters. P - seconds. G - m^3. kg^-. s^-2. pi - no units.

Match the descriptions to either g or G.

g : stands for surface gravity on Earth. is an acceleration. can be used o compare weight on different planets. G: is used in Newton's law of gravity. is the same everywhere in the universe.

Select the descriptions to either g or G.

g: The acceleration of gravity near a plaent's surface. 9.8 m/s^2 on Earth. G: A constant in Newton's law of gravity. = 6.67 x 10^-11 m^3 kg^-1 s^-2

Newton's __________ law of motion states that the ________ acting on an object must be the product of the ____________ and the acceleration of the object.

second ; force ; mass.

A gun fires a dart, and the dart appears to be accelerated much more strongly than the gun. This is an example of Newton's _________ law.

second. (Newton's second law states: "The acceleratin of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object." This gives us the equation F = ma.)

M = dV^2 / G. Based on the equation, we can conclude that moons that are farther out from a planet have ___________.

slower orbital speeds. (Larger orbits must have smaller orbital velocities, so that dV^2/G remains constant.)

Match the constants and variables on the left to the equations they apply to on the right.

G -> Newton's law of gravity. P -> Kepler's third law of planetary motion. a -> Newton's second law of motion.

The mass of Mercury was determined by:

The gravitational attraction exerted by Mercury on a Spacecraft.

The moon orbits Earth, but a falling apple hits the ground. This is because ______

the Moon also has a "sideways" (conpared to falling) velocity. (If the apple were moving sideways (at a right angle to the direction toward Earth) at a very high rate of speed, it too would orbit.)

The strength of the gravitational force exerted by Earth on you is the same as the strength of the gravitational force exerted by you on Earth.

true?

A planet with 9 times the mass and _______ times the radius of Earth will have the same surface gravity as Earth.

3. (3 squared is 9, and this gives 9 over 9 in the equation.)

If you apply a force F to a mass m, it results in an acceleration a. What acceleration would result if you applied a force to 10F to 3m?

3.33a.

For the same radius, the larger a planet's mass, the _______ the escape velocity.

Greater.

Newton's __________ law of motion is that two interacting bodies produce a pair of equal and opposite forces on each other.

Third.

Two spaceships are ready to lift-off from the surface of Mercury. Spaceship I requires a speed of 4.3km/s to escape from Mercury. Spacechip II is twice as heavy as Spaceship I. How much speed is required for Spaceship II to escape from Mercury?

4.3 km/s

If you apply a force F to a mass m, it results in acceleration a. What acceleration would result if you applied a force to 6F to m?

6a.

Two planets have identical diameters but differ in mass by a factor of 81. The more massive planet therefore has an escape velocity ___________ than the other.

9 times larger.

What kind of object has an escape velocity equal to the speed of light?

A black hole.

___________ velocity is the speed an object must attain to break free of orbit.

Escape.

An astronaut floating in space throws a wrench, exerting a 20 N force. The astronaut ______.

experience a 20 N force in the opposite direction. (Newton's third law requires that the force be equal and opposite.)

Observing the effect of gravity between a planet and its moon can allow us to determine the planet's _________.

mass.

A Moon rock has a mass of 2 kg. What is the mass of the same rock when brought to Earth?

2 kg.

The Earth has an arrow pointing towards the Moon, while the Moon has an arrow pointing towards the Earth. The Moon's arrow is much longer than the Earth's arrow. Both arrows are labeled with the letter a. Each has an arrow pointing perpendicularly to the other arrows. The moons other arrow is much longer than Earth's other arrow. True or false: in the diagram, the force of gravity exerted by the planet on the Moon is stronger than the force of gravity exerted by Moon on the planet.

False. (Using Newton's law of gravity shows that the two forces are equal. Remember F= GMm/r^2; for both forces, the masses and distance are the same.

If all objects on Earth are acted on by the force of gravity (giving them weight), how is it that an object can remain stationary (be at constant velocity)?

For an object to remain stationary, gravity must be balanced by other forces. (No net force = no change in velocity.)

The idea that a force exists between two bodies that depends on the product of their masses and the square of the distance between them was formalized by ___________ and is known as the universal law of __________.

Newton ; Gravitation.

A coconut falling from a tree is an example of _________

Newton's second law of motion. (The force of gravity causes the apple to accelerate.)

The Earth has an arrow pointing towards the Moon, while the Moon has an arrow pointing towards the Earth. The Moon's arrow is much longer than the Earth's arrow. Both arrows are labeled with the letter a. Which idea or equation be explains the different accelerations (arrows) shown in the picture?

Newton's second law: a=F/m (The same force accelerates a smaller mass more.

Select the planets that would have the same surface gravity as Earth.

One with nine times the mass and three times the radius.

Who was the first person to suggest that gravity is what keeps the planets in their orbits around the Sun?

Robert Hooke

Match each example of motion with whether it is a speed or a velocity.

Speed : 88 mph, 4 cm/yr Velocity: 1000 km/s north, 11.4 km/s up

__________ is the term for the acceleration of gravity near a body's surface.

Surface gravity.

As a rocket burns its fuel to accelerate, it gets less and less massive. If the force produced by the engine stayed constant, what does Newton's second Law tell us about the motion?

The acceleration would increase. (Acceleration is inversely proportional to mass, so if the mass decreased, the acceleration would increase.)

A rocket blasts propellant out of its thrusters and "lifts off", heading into space. What provided the force to lift the rocket?

The action of the propellant accelerating down, giving a reaction force to the rocket.

Match each object with the force that would be needed to accelerate it to 5 m/sec^2.

- 0.750 N -> A 0.150 kg baseball. - 500 N -> A 100 kg person. - 15,000 N -> A 3000 kg sport utility vehicle. - 10^31 N -> The Sun, with mass 2 x 10^30 kg. *a=F/m so acceleration (5 m/sec^2), F (Net Force [N]), m (Mass).

A cannon mounted on the Earth at the north pole fires a projectile parallel to the surface. Three paths for the projectile are visible: One short path falling to the Earth, the second falling after traversing above about one-quarter of the surface, and the third circling the Earth maintaining its height above the surface. This demonstrates ________

- "Newton's cannon", a thought experiment. - How something can be forever falling but not hit Earth.

Select all that represent an object undergoing an acceleration.

- A ball falling off a table. (The falling ball is accelerated by gravity.) - A car braking to a stop. (Any change in velocity is an acceleration.) - A car turning a corner at 88 km/hr. (A change in direction is an acceleration.)

Which of the following demonstraes the property of inertia? Select all that apply.

- A car skidding on a slippery road. - The oil tanker Exxon Valdez not being able to stop and running aground. - A brick sitting on a tabletop. - Whipping a tablecloth out from under the dishes set on a table.

Select the cases in which the object undergoes acceleration.

- A car slowing down with the brakes on. (Any change in speed is an acceleration.) - A leaf falling from a tree. (The falling leaf is accelerated by gravity.) - The Moon orbiting Earth. (Orbiting objects constantly change direction [they are accelerated].)

Select all the objects that (essentially) maintain a constant velocity.

- A hockey puck sliding on the ice. - An apple sitting on a table. (an object that isn't moving has a constant velocity-zero.)

Select all the examples below where the net force is zero.

- A spacecraft in deep space at constant velocity. (With no acceleration from its rockets, or gravity from nearby objects, the net force on the spacecraft is zero.) - A box sitting on a table. (Earth's gravity pulling down on the box is balanced by the force of the table pushing up on the box.) - Two people pushing on opposite sides of a box with equal strength.

Select all the choices that describe escape velocity.

- It's equal to square root of 2GM/R. - It's the speed required to escape a body's gravity.

Which of the following statements apply to a truck that is moving up a steep, straight hill at a constant speed of 10 km/hour. Select all that apply.

- The truck obeys Newton's second law. - There is no net force on the truck. - The truck is not accelerating.

Select all of the statements that correctly describe the constant G in Newton's universal law of gravity.

- The value of G is 6.67 in x 10^-11 Nm^2/kg^2. (A Newton [N] equal kgm/s^2.) - G is the same everywhere in the universe. - G is essentially a conversion factor.

Select the cases that correctly describe orbiting objects.

- Two equally massive bodies orbit each other equally. (You can show that accelerations are equal by equating the force of gravity formula to F = m x a for each object. - When one object is very massive compared to the other object, the center of the balance point of the orbit can be inside the massive object. - As a result of Newton's second and third laws, the smaller body moves more. ( You can show that the smaller body has a larger acceleration by equating the force of gravity formula to F = m x a for each object.)

If an object moves along a curved path at a constant speed, you can infer that

- a force is acting on it. - it is accelerating.

A person twirls a ball on a string in a circle above their head. One arrow points inward along the string towards their hand, while another arrow is tangent to the circle made by the ball. The ball will move faster if the person _________.

- let's out some string and exerts the same force. - exerts a stronger force on the string.

You release a ball that rolls downhill on a curbing ramp. This is considered "accelerated motion" because _________

- the ball's speed is changing (acceleration produces a change in speed, direction, or both.) - the ball's direction is changing (acceleration produces a change in speed, direction, or both.)

A rocket is in orbit around Earth. This means _______.

- the force to hold the rocket in orbit is provided by gravity. - if the rocket fires its engine and changes its V, its orbit will change. (If V changes, Fcircular would no longer equal FG and the orbit would change.)

Astronomers might use the modified version of Kepler's third law to determine ________.

- the total mass of a binary star system. (The mass of the stars can be determined using Kepler's third law.) - the mass of a nearby star with planets. ( The planet's orbits can be used to find the mass of the star.) - the mass of a Kuiper belt dwar planet and its moon. (The mass of the planet and the moon could be found using Kepler's third law.)

The force needed to keep an object moving in a circle (not necessarily an orbit) depends on ________.

- the velocity of the object - the object's mass - the radius of the circle

Asronatus sometimes train in water tanks because the buoyancy of water exerts a force that opposes the pull of Earth's gravity. In the tank, the __________ of the astronauts and their equipment decreases, but the _____________, which affects how hard it is to move them, stays the same.

- weight. - inertia.

Compare the surface gravity of Earth with the surface gravities of Jupiter and Pluto. Radius of Jupiter = 11.9 times radius of Earth. Radius of Pluto = 0.181 times radius of Earth. Mass of Jupiter = 317.9 times mass of Earth. Mass of Pluto = 0.00210 times mass of Earth. Earth's surface gravity is about _____ times Jupiter's. Earth's surface gravity is about _____ times Pluto's.

0.394. 15.6

The same force is applied to all the objects. Arrange them according to how much acceleration they experience, from the most (top) to the least (bottom).

1. A Ping-Pong Ball. 2. A tennis ball. 3. A bowling ball. 4. A golf cart.

Rank the following objects by how much inertia they have, from least (top) to most (bottom).

1. A leaf falling from a tree. 2. A car driving on the highway. 3. A house. 4. The Moon orbiting Earth. 5. The Sun. *Inertia: a property of matter by which it continues in its existing state of rest or uniform motion in a straight line, unless that state is changed by an external force.

Arrange the statements to show that the velocity of an orbiting moon can be used to measure the mass of a planet, even though the force to hold the orbit depends only on the moon's mass.

1. The moon must be in circular orbit. 2. Since the moon is in a circular orbit, the force of gravity provides the force that makes the moon orbit. 3. Forbit=Fgravity. 4. Solving for V,

If quantity A is directly proportional to quantity B, then if B increases 10 times, A must increase ___________ times.

10.

Reducing the separation of two bodies to one-fourth its original value will cause the gravitational force between them to become ______ times __________.

16 ; stronger.

A planet with four times the mass and half the radius of Earth will have surface gravity ________ times stronger than Earth.

16. (It's 4 times stronger because of the mass, and (1/(1/2)^2)=4 times stronger because of the radius, for a total of 4x4=16 times stronger.)

Assuming the mass of the Milky Way Galaxy is 10^11 times that of the Sun and that the Sun is 2.64 x 10^20m from its center, what is the Sun's orbital speed around the center of the Galaxy? Express your answer in the order of 10^5m/s. answer: How long does it take the Sun to orbit the center of the Milky Way? Express your answer in million years. answer: (In this problem, we assume that the Galaxy can be treated as a single large mass. This isn't correct, but the more elaborate math needed to calculate the problem properly ends up giving almost the same answer.)

2.24V 230 million years.

Suppose that a planet was discovered that has 4 times the mass of Earth, and the same diameter as Earth. Assume that for Earth the escape velocity is 11 km/s. What would be the escpae velocity for this planet?

22 km/s.

The gravitational force between two asteroids is 100 N. If the distance between them doubles, the gravitational force will be ________.

25 N. (The distance has doulbed so the force is 1/4 as great.)

If you apply a force F to mass m, it results in an acceleraion a. What acceleration would result when you apply a force 6F to 2m?

3a. a = F / m.

Match the escape velocity with the object. (Hint: Think about what escape veloctiy depends on.)

3x10^5 km/sec ------ A black hole (at the horizon). 617 km/sec ---------- The Sun ( at the surface). 42 km/sec ----------- The Sun (at Earth's orbit). 11.2 km/sec----------- Earth (at the surface). 2.4 km/sec ----------- The Moon (at the surface).

If Earth were 16 times as far from the Sun as it is, Earth's orbital velocity would be about ____________ times slower.

4.

You apply a 12 N force to a 3 kg mass. The acceleration it produces is ___________.

4. (a = F/m. a = 12/3. a = 4 m/s^2.)

Match the terms and definitions.

Acceleration - A change in speed, direction, or both. Velocity - The speed and direction of an object. Mass - The amount of matter in an object. Force - Something that causes a change in speed, direction, or both.

Which of the following apples is accelerating the most?

All accelerate at the same rate.

Earth's shape is somewhat flattened, so that the diameter through the poles is shorter than the diameter of the equator. Where would you weigh more?

At the poles.

If two planets have the same mass, but one has four times the radius of the other, how will their escape velocities compare?

The larger planet will have one-half the escape velocity of the small planet. (Radius is in the denominator of the escape velocity equation.)

Two planets are experiencing the same force, but one is twice as massive as the other. Which planet has the highest acceleration?

The less massive planet. (acceleration is inversely proportional to mass.)

If two planets have the same mass, but one has four times the raidus of the other, how will their escape velocities compare?

The more massive planet has an escape velocity three time larger than the less massive planet. (Escape veloctiy is proportional to the square root of the mass.)

If two planets have the same radius, but one has nine times more mass than the other, how do their escape velocities compare?

The more massive planet has an escape velocity three times larger than the less massive planet. (Escape velocity is proportional to the square root of the mass.)

Which of the following statements is true about a hockey puck moving on ice in a straight line at constant speed?

The net force on the puck is zero.

True or false: If astronomers know the period and semimajor axis of the orbit of a planet circling a nearby star and have some independent way to determine the mass of the star, they have enough information to determine the mass of the planet.

True. (Using Kepler's third law, they could find the sum of the star's and planet's masses. If they know the mass of the star, this could be subtracted to leave the mass of the planet.

The force to keep an object turning in a circle is given by F=mxV^2/d. How much more force is required for a planet to keep a moon in an orbit of the same distance and speed if the moons mass were to double?

Twice as much force.

Newton's law of inertia states that a moving body maintains a constant __________, moving in a ____________ line, unless a ___________ acts on it.

Velocity; straight; force.

Near the surface of Earth, g=9.8m/s^2. At a height of 6400 km above Earth's surface (one Earth radius), the acceleration of gravity would be _________.

about one-quarter as much. (6400 km above the surface is twice as far from the center, and R is squared.)

If the distance between two bodies is increased by a factor of 4, the gravitational force between them is _____ by a factor of _________.

decreased ; 16.

A car turns a corner, and the Moon orbits Earth. There is more inertia overcome in changing the Moon's direction because ___________

it is much more massive. (The more mass, the more inertia.)

If a spacecraft launched from Earth doesn't have sufficient velocity, _________.

it won't break free of Earth's gravity. (The spacecraft has to be going faster than the escape velocity.)

The speed of an object is how fast it moves--how far it goes over a period of time. The velocity of an object is _____

its speed and the direction it travels.

The surface gravity of a planet with twice the mass and twice the radius of Earth will be ______ surface gravity of Earth.

less than. (The radius is sqaured but the mass isn't.)

Mars completes one orbit around the Sun in approximately two Earth years. Mars orbits at an average distance to the Sun of about 1.5 AU, and Mars' mass is about 1/10 of Earth's mass. Therefore, Mars' orbital speed is ________ the orbital speed of Earth.

lower than.

The escape velocity from a celestial body depends on the __________ of the body and the ________ from the center of the body.

mass ; radius.

M = V^2d/G = (2pid/P)^2 d/G = 4pi^2d^3/ GP^2. If you are using the equation at the right to calculate the mass of a star based on the motion of a planet and if the units of Newton's constant G are m^3 kg^-1 s^-2, what should the units of d and P be?

meters and seconds

If one planet is larger (in size) than another, its surface gravity _______.

might or might not be bigger. (It would depend on the densities of the two planets.)

If two objects are accelerated to the same velocity, the more massive object requires __________ force.

more. (Since a=F/m, for a bigger m you need a correspondingly larger F to get the same a.)

The force to keep an object turning in a circle is given by F = m x V^2/d. You swing a ball on a string. The same force is required to swing the ball three times as fast (3V) at distance d as is requied to swing it at speed V at __________ the distance.

one-ninth. (V -> 3V makes the force go up 9 times [V is squared and on top.] d -> 1/9d would have the same effect [d is not squared and is on the bottom of the fraction.])

A rocket ship in space fires its engine. The force that accelerates it is from __________.

the reaction to rocket fuel exploding out the back of the ship. (The force pushing on the ship forward is equal and opposite to the force accelerating the burning fuel out the back.)

Match the correct missing words with each statement.

the same as ---- A truck falling off a bridge will experience an acceleration that is _________ a pebble that falls off. larger than ---- The pull of gravity from Earth on a truck is ____________ that on a pebble. smaller than ---- Very far from Earth's surface, the acceleration of gravity is _________ it is close to the surface.

An astronaut has a mass of 60 kilograms before she takes off in her ship. When she reaches Earth's orbit, her mass is __________; when she lands on the Moon, her mass is __________.

the same as on Earth; the same as on Earth.

Two asteroids, R and S, orbit each other. R is 10 times the mass of S. Compared to the gravitational force exerted by R pulling S toward R, the gravitational force exerted by S pulling R toward S is __________.

the same. (Gravity is between two massess and depends on both of them. Each pulls on the other with the same strength but in opposite directions [Newton's third law]).

A gun fires a dart, and the dart and the gun exeperience forces in opposite directions. This is an example of Newton's ________ law.

third.

M = dV^2/G. An orbit that is nine times farther from a black hole will have a circular velocity that is _______ than the closer orbit.

three times slower. (If d increases by a factor of nine, V must decrease by square root of 9 = 3.)

If the period and separation of binary stars are known, then a modified version of Kepler's third law can be used to determine the system's _________.

total mass. (The third law relates mass, separation, and period.)

Compared to the gravitational force between two bodies with masses of 100 kig and 200 kg, the gravitational force between two bodies the same distance apart with masses of 100 kg and 400 kg is ________

twice as much. (Force is directly proportional to the product of the masses - which is not twice as much).

If the same force acts on one cart with a mass of 5 kg and another with a mass of 10 kig, the 5 kg cart will be accelerated _______ as much as the 10 kg cart.

twice. (For the same force, half the mass will result in twice the acceleration.)

A dropped apple falls because of the force of gravity between it and Earth. Compared to the downward force on the apple, the force on Earth is _________.

upward and equal. (The apple and the Earth exert equal forces on each other.)

Compared to being on Earth, on Mars your ________

weight will be different and your mass the same (Weight depends on the pull of gravity. Mass depends on how much matter is in an object.)

If the gravitational force between Earth and the Moon were suddenly switched off, the Moon's motion ________

would be a straight line (In the absence of a force, inertia keeps the Moon moving straight.)