Define Newton's law of universal gravitation .

Newton's law of universal gravitation states that the gravitational force between two objects is directly proportional to each of their masses and inversely proportional to the square of the distance between their centers of mass.

The mass of a uniform sphere can be treated as a point mass at its .......... .

The mass of a uniform sphere can be treated as a point mass at its center .

True or False? Doubling the distance between two masses halves the gravitational force between them.

False. The force is inversely proportional to the square of the distance, so doubling the distance reduces the force to one quarter .

What is the direction of the gravitational force between two objects?

The force is attractive : it pulls the objects together .

Along which line is the gravitational force between two systems exerted?

Along the line connecting the centers of mass of the two interacting systems.

The gravitational force on a system can be considered to be exerted on the system's .......... .

The gravitational force on a system can be considered to be exerted on the system's center of mass .

True or False? Gravitational force acts only between very large objects such as planets.

False. There is a universal force of attraction between all matter with mass ; it is just almost negligible for objects with a small mass such as atoms.

What is the range of the gravitational force?

The range is infinite , so gravitational force affects all objects in the universe.

What provides the centripetal force that keeps the Moon in a circular orbit around the Earth?

The Earth's gravitational force on the Moon.

When can the gravitational force between two systems be considered constant as their relative position changes?

When the change in the relative position of their centers of mass causes only a negligible change in the gravitational force The force is then treated as constant at all points between the initial and final positions

Define gravitational field .

A gravitational field is a region of space where a mass experiences a force due to the gravitational attraction of another mass.

What does a field model?

The effects of a noncontact force exerted on an object at various positions in space.

What do gravitational field lines show?

The direction of the gravitational force that would be exerted on a mass placed at that position The direction of acceleration of a point mass placed in the field

The closer together the field lines are, the .......... the gravitational field.

The closer together the field lines are, the stronger the gravitational field.

Describe the gravitational field around a point mass.

The field is radial The field lines point toward the center of the mass The field is non-uniform : the field strength changes with distance from the center

How is a uniform gravitational field represented?

By equally spaced parallel field lines The field strength is the same at all points, for example near Earth's surface

True or False? Gravitational field lines around the Earth point away from its center.

False. Gravitational forces are attractive only , so the field lines point toward the center of the Earth.

Define acceleration due to gravity .

Acceleration due to gravity is the observed acceleration of an object when the gravitational force is the only force exerted on it. It is numerically equal to the magnitude of the gravitational field strength at that location.

Why is the only force on an object falling in a vacuum its weight ?

A vacuum contains no matter , so there are no particles to exert frictional forces such as air resistance on the object.

When air resistance is .......... , a falling object can be approximated as falling in a vacuum.

When air resistance is negligible , a falling object can be approximated as falling in a vacuum.

Why do objects of different mass and surface area fall differently through air?

Air resistance is a frictional force from collisions with air particles, and its effect differs with an object's surface area and mass , so the accelerations differ.

The magnitude of the gravitational field at a point is the .......... of the gravitational force on a test object to the test object's .......... .

The magnitude of the gravitational field at a point is the ratio of the gravitational force on a test object to the test object's mass .

Weight is the gravitational force exerted by an astronomical body on a relatively small nearby object .

Mass is a measure of an object's .......... .

Mass is a measure of an object's inertia .

True or False? A person's mass is less on the Moon than on Earth.

False. Mass is the same everywhere in the universe. Weight is less on the Moon because the gravitational field strength is less.

What determines the weight of an object at a given position?

The magnitude of the gravitational field at the object's position, so the same mass has a greater weight in a stronger field.

When does a system appear weightless ?

When no forces are exerted on it (infinitely far from any other object) When the force of gravity is the only force exerted on it (free fall)

Why do astronauts in orbit predominantly experience weightlessness ?

They are in continuous free fall around the Earth, so the normal force between them and any surface is zero .

When the acceleration is in the opposite direction to the weight, the apparent weight is .......... than the actual weight.

When the acceleration is in the opposite direction to the weight, the apparent weight is greater than the actual weight.

True or False? A scale in an elevator that is moving upward but slowing down reads more than the actual weight.

False. The elevator is slowing while moving upward, so its acceleration is downward , in the same direction as the weight. The scale reads less than the actual weight.

Define non-inertial reference frame .

A non-inertial reference frame is a reference frame that is accelerating with respect to an inertial reference frame.

State the equivalence principle for gravitational force.

An observer in a non-inertial reference frame cannot distinguish between an object's apparent weight and the gravitational force exerted on it by a gravitational field.

Define inertial mass .

Inertial mass is the property ( inertia ) that determines how much an object's motion resists changes when interacting with another object.

Define gravitational mass .

Gravitational mass is the property of a system with mass that determines the force of attraction between it and another system with mass.

How can inertial mass be measured?

Apply a force to accelerate the mass Commonly, set the mass oscillating on a spring of spring constant k and find the time period from the time for 10 oscillations

How can gravitational mass be measured?

Place the object in a gravitational field and measure the gravitational force on it Commonly, use balance scales : the masses needed to balance it equal its gravitational mass

Which law is used to calculate inertial mass and which to calculate gravitational mass ?

Inertial mass : Newton's second law Gravitational mass : Newton's law of gravitation

Inertial mass and gravitational mass have been experimentally verified to be .......... .

Inertial mass and gravitational mass have been experimentally verified to be equivalent .

AP®PhysicsCollege BoardPhysics 1: Algebra-BasedFlashcardsUnit 2: Force & Translational DynamicsGravitational Force

Gravitational Force (College Board AP® Physics 1: Algebra-Based): Flashcards

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FrontNewton's Law of Gravitation
Define Newton's law of universal gravitation.
FrontNewton's Law of Gravitation
State the equation for Newton's law of universal gravitation.
BackNewton's Law of Gravitation
$|\vec{F_{g}}| = G \frac{m_{1} m_{2}}{r^{2}}$
$|\vec{F_{g}}|$ = magnitude of the gravitational force (N)
$G$ = universal gravitational constant (N·m²/kg²)
$m_{1}$ = mass of object 1 (kg)
$m_{2}$ = mass of object 2 (kg)
$r$ = distance between the centers of mass (m)

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Cards in this collection (54)

Define Newton's law of universal gravitation.
Newton's law of universal gravitation states that the gravitational force between two objects is directly proportional to each of their masses and inversely proportional to the square of the distance between their centers of mass.
State the equation for Newton's law of universal gravitation.
$|\vec{F_{g}}| = G \frac{m_{1} m_{2}}{r^{2}}$
- $|\vec{F_{g}}|$ = magnitude of the gravitational force (N)
- $G$ = universal gravitational constant (N·m²/kg²)
- $m_{1}$ = mass of object 1 (kg)
- $m_{2}$ = mass of object 2 (kg)
- $r$ = distance between the centers of mass (m)
State the value of the universal gravitational constant.
$G = 6.67 \times 10^{- 11}$ N·m²/kg²
A satellite orbits at a height h above the surface of a planet of radius R. What is the value of r in Newton's law of universal gravitation?
$r = R + h$
The distance r is measured from the center of the planet, not from its surface.
The mass of a uniform sphere can be treated as a point mass at its ...........
The mass of a uniform sphere can be treated as a point mass at its center.
True or False?
Doubling the distance between two masses halves the gravitational force between them.
False.
The force is inversely proportional to the square of the distance, so doubling the distance reduces the force to one quarter.
What is the direction of the gravitational force between two objects?
The force is attractive: it pulls the objects together.
Along which line is the gravitational force between two systems exerted?
Along the line connecting the centers of mass of the two interacting systems.
The gravitational force on a system can be considered to be exerted on the system's ...........
The gravitational force on a system can be considered to be exerted on the system's center of mass.
True or False?
Gravitational force acts only between very large objects such as planets.
False.
There is a universal force of attraction between all matter with mass; it is just almost negligible for objects with a small mass such as atoms.
What is the range of the gravitational force?
The range is infinite, so gravitational force affects all objects in the universe.
What provides the centripetal force that keeps the Moon in a circular orbit around the Earth?
The Earth's gravitational force on the Moon.
When can the gravitational force between two systems be considered constant as their relative position changes?
- When the change in the relative position of their centers of mass causes only a negligible change in the gravitational force
- The force is then treated as constant at all points between the initial and final positions
Define gravitational field.
A gravitational field is a region of space where a mass experiences a force due to the gravitational attraction of another mass.
What does a field model?
The effects of a noncontact force exerted on an object at various positions in space.
What do gravitational field lines show?
- The direction of the gravitational force that would be exerted on a mass placed at that position
- The direction of acceleration of a point mass placed in the field
The closer together the field lines are, the .......... the gravitational field.
The closer together the field lines are, the stronger the gravitational field.
Describe the gravitational field around a point mass.
- The field is radial
- The field lines point toward the center of the mass
- The field is non-uniform: the field strength changes with distance from the center
How is a uniform gravitational field represented?
- By equally spaced parallel field lines
- The field strength is the same at all points, for example near Earth's surface
True or False?
Gravitational field lines around the Earth point away from its center.
False.
Gravitational forces are attractive only, so the field lines point toward the center of the Earth.
Define acceleration due to gravity.
Acceleration due to gravity is the observed acceleration of an object when the gravitational force is the only force exerted on it. It is numerically equal to the magnitude of the gravitational field strength at that location.
State the value of the acceleration due to gravity near Earth's surface.
$g \approx 10$ m/s²
Why is the only force on an object falling in a vacuum its weight?
A vacuum contains no matter, so there are no particles to exert frictional forces such as air resistance on the object.
When air resistance is .........., a falling object can be approximated as falling in a vacuum.
When air resistance is negligible, a falling object can be approximated as falling in a vacuum.
True or False?
In a vacuum, a heavier object falls with a greater acceleration than a lighter object.
False.
In a vacuum the only force is weight, so $a = \frac{m g}{m} = g$ . The mass cancels, so every object accelerates at $g$ regardless of its mass.
Why do objects of different mass and surface area fall differently through air?
Air resistance is a frictional force from collisions with air particles, and its effect differs with an object's surface area and mass, so the accelerations differ.
The magnitude of the gravitational field at a point is the .......... of the gravitational force on a test object to the test object's ...........
The magnitude of the gravitational field at a point is the ratio of the gravitational force on a test object to the test object's mass.
State the equation for gravitational field strength in terms of force and mass.
$| \vec{g} | = \frac{| F_{g} |}{m}$
- $| \vec{g} |$ = gravitational field strength (N/kg)
- $| F_{g} |$ = gravitational force on the test object (N)
- $m$ = mass of the test object (kg)
State the equation for gravitational field strength in terms of the mass of the system creating the field.
$| \vec{g} | = G \frac{M}{r^{2}}$
- $G$ = universal gravitational constant (N·m²/kg²)
- $M$ = mass of the system creating the field (kg)
- $r$ = distance from the center of that system to the point in the field (m)
When the Moon orbits the Earth, which body is the system creating the gravitational field and which is the test object?
- The Earth (mass $M$ ) is the system that creates the field
- The Moon (mass $m$ ) is the test object in the field
Which two laws are combined to derive the gravitational field strength equation?
- Newton's second law, with $a = |g|$ when gravity is the only force
- Newton's law of gravitation
True or False?
Gravitational field strength at a point depends on the mass of the test object.
False.
The test object's mass cancels, so $| g | = G \frac{M}{r^{2}}$ depends only on the mass of the system creating the field and the distance from it.
Define weight.
Weight is the gravitational force exerted by an astronomical body on a relatively small nearby object.
State the equation for weight.
$weight = |\vec{F_{g}}| = m g$
- $|\vec{F_{g}}|$ = magnitude of the gravitational force on the object (N)
- $m$ = mass of the object (kg)
- $g$ = gravitational field strength (N/kg)
Mass is a measure of an object's ...........
Mass is a measure of an object's inertia.
True or False?
A person's mass is less on the Moon than on Earth.
False.
Mass is the same everywhere in the universe. Weight is less on the Moon because the gravitational field strength is less.
What determines the weight of an object at a given position?
The magnitude of the gravitational field at the object's position, so the same mass has a greater weight in a stronger field.
When does a system appear weightless?
- When no forces are exerted on it (infinitely far from any other object)
- When the force of gravity is the only force exerted on it (free fall)
Why do astronauts in orbit predominantly experience weightlessness?
They are in continuous free fall around the Earth, so the normal force between them and any surface is zero.
Define apparent weight.
The apparent weight of a system is the magnitude of the normal force exerted on the system.
$apparent weight = | \vec{F_{n}} |$
What does a scale read for a system that is stationary or moving at constant speed?
Its actual weight, because the apparent weight equals the actual weight.
$| \vec{F_{n}} | = m g$
How does apparent weight compare with actual weight when the acceleration is in the same direction as the weight?
Apparent weight is less than actual weight.
$| \vec{F_{n}} | = m g - m a$
When the acceleration is in the opposite direction to the weight, the apparent weight is .......... than the actual weight.
When the acceleration is in the opposite direction to the weight, the apparent weight is greater than the actual weight.
True or False?
A scale in an elevator that is moving upward but slowing down reads more than the actual weight.
False.
The elevator is slowing while moving upward, so its acceleration is downward, in the same direction as the weight. The scale reads less than the actual weight.
Define non-inertial reference frame.
A non-inertial reference frame is a reference frame that is accelerating with respect to an inertial reference frame.
State the equivalence principle for gravitational force.
An observer in a non-inertial reference frame cannot distinguish between an object's apparent weight and the gravitational force exerted on it by a gravitational field.
An elevator far from any gravitational field accelerates at 10 m/s². What can a person inside it conclude?
They cannot tell the difference between this and being stationary on Earth, where $g = 10$ m/s². In both cases, dropped objects fall at 10 m/s² relative to the elevator.
Define inertial mass.
Inertial mass is the property (inertia) that determines how much an object's motion resists changes when interacting with another object.
Define gravitational mass.
Gravitational mass is the property of a system with mass that determines the force of attraction between it and another system with mass.
How can inertial mass be measured?
- Apply a force to accelerate the mass
- Commonly, set the mass oscillating on a spring of spring constant k and find the time period from the time for 10 oscillations
How can gravitational mass be measured?
- Place the object in a gravitational field and measure the gravitational force on it
- Commonly, use balance scales: the masses needed to balance it equal its gravitational mass
Which law is used to calculate inertial mass and which to calculate gravitational mass?
- Inertial mass: Newton's second law
- Gravitational mass: Newton's law of gravitation
Inertial mass and gravitational mass have been experimentally verified to be ...........
Inertial mass and gravitational mass have been experimentally verified to be equivalent.
True or False?
An object acted on only by gravity accelerates at a rate equal to the magnitude of the gravitational field strength.
True.
Inertial and gravitational mass are the same, so the object's mass cancels in $m a = G \frac{M m}{r^{2}}$ , leaving $a = G \frac{M}{r^{2}} = |\vec{g}|$ .

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