CP Workbook
Gravitational Interactions
Printer Friendly Version
The equation for the law of universal gravitation is
where
F
is the attractive force between masses
m
_{1}
and
m
_{2}
separated by distance
d
.
G
is the universal gravitational constant and relates
F
to the masses and distance as the constant π similarly relates the circumference of a circle to its diameter.
By substituting changes in any of the variables into this equation, we can predict how the others change. For example, we can see how the force changes if we know how either or both of the masses change, or how the distance between their centers changes.
Suppose, for example, that one of the masses somehow is doubled. Then substituting 2m
_{1}
for m
_{1}
in the equation gives
So we see the force doubles also. Or suppose instead that the distance of separation is doubled. Then substituting 2d for d in the equation gives
And we see the force is only ¼ as much.
Use this method to solve the following problems. Write the equation and make the appropriate substitutions.
If both masses are doubled, what happens to the force?
If the masses are not changed, but the distance of separation is reduced to ½ the original distance, what happens to the force?
If the masses are not changed, but the distance of separation is reduced to ¼ the original distance, what happens to the force?
If both masses are doubled, and the distance of separation is doubled, show what happens to the force.
If one of the masses is doubled, the other remains unchanged, and the distance of separation is tripled, show what happens to the force.
Consider a pair of binary stars that pull on each other with a certain force. Would the force be larger or smaller if the mass of each star were three times as great when their distance apart is three times as far? Describe how the new force will be compared to the first one.
Related Documents
Lab:
Labs -
Coefficient of Friction
Labs -
Coefficient of Friction
Labs -
Coefficient of Kinetic Friction (pulley, incline, block)
Labs -
Conservation of Momentum in Two-Dimensions
Labs -
Falling Coffee Filters
Labs -
Force Table - Force Vectors in Equilibrium
Labs -
Gravitational Field Strength
Labs -
Inelastic Collision - Velocity of a Softball
Labs -
Inertial Mass
Labs -
Kepler's 1st and 2nd Laws
Labs -
Lab: Triangle Measurements
Labs -
LabPro: Newton's 2nd Law
Labs -
Loop-the-Loop
Labs -
Mars' Lab
Labs -
Mass of a Rolling Cart
Labs -
Moment of Inertia of a Bicycle Wheel
Labs -
Relationship Between Tension in a String and Wave Speed
Labs -
Relationship Between Tension in a String and Wave Speed Along the String
Labs -
Static Equilibrium Lab
Labs -
Static Springs: Hooke's Law
Labs -
Static Springs: Hooke's Law
Labs -
Static Springs: LabPro Data for Hooke's Law
Labs -
Terminal Velocity
Labs -
Video LAB: A Gravitron
Labs -
Video LAB: Ball Re-Bounding From a Wall
Labs -
Video Lab: Falling Coffee Filters
Resource Lesson:
RL -
Advanced Gravitational Forces
RL -
Advanced Satellites
RL -
Air Resistance
RL -
Air Resistance: Terminal Velocity
RL -
Forces Acting at an Angle
RL -
Freebody Diagrams
RL -
Gravitational Energy Wells
RL -
Gravitational Potential Energy
RL -
Inclined Planes
RL -
Inertial vs Gravitational Mass
RL -
Newton's Laws of Motion
RL -
Non-constant Resistance Forces
RL -
Properties of Friction
RL -
Springs and Blocks
RL -
Springs: Hooke's Law
RL -
Static Equilibrium
RL -
Systems of Bodies
RL -
Tension Cases: Four Special Situations
RL -
The Law of Universal Gravitation
RL -
Universal Gravitation and Satellites
RL -
Universal Gravitation and Weight
RL -
What is Mass?
RL -
Work and Energy
Review:
REV -
Review: Circular Motion and Universal Gravitation
Worksheet:
APP -
Big Fist
APP -
Family Reunion
APP -
The Antelope
APP -
The Box Seat
APP -
The Jogger
CP -
Action-Reaction #1
CP -
Action-Reaction #2
CP -
Equilibrium on an Inclined Plane
CP -
Falling and Air Resistance
CP -
Force and Acceleration
CP -
Force and Weight
CP -
Force Vectors and the Parallelogram Rule
CP -
Freebody Diagrams
CP -
Incline Places: Force Vector Resultants
CP -
Incline Planes - Force Vector Components
CP -
Inertia
CP -
Mobiles: Rotational Equilibrium
CP -
Net Force
CP -
Newton's Law of Motion: Friction
CP -
Static Equilibrium
CP -
Tensions and Equilibrium
NT -
Acceleration
NT -
Air Resistance #1
NT -
An Apple on a Table
NT -
Apex #1
NT -
Apex #2
NT -
Falling Rock
NT -
Falling Spheres
NT -
Friction
NT -
Frictionless Pulley
NT -
Gravitation #1
NT -
Head-on Collisions #1
NT -
Head-on Collisions #2
NT -
Ice Boat
NT -
Rotating Disk
NT -
Sailboats #1
NT -
Sailboats #2
NT -
Scale Reading
NT -
Settling
NT -
Skidding Distances
NT -
Spiral Tube
NT -
Tensile Strength
NT -
Terminal Velocity
NT -
Tug of War #1
NT -
Tug of War #2
NT -
Two-block Systems
WS -
Advanced Properties of Freely Falling Bodies #1
WS -
Advanced Properties of Freely Falling Bodies #2
WS -
Advanced Properties of Freely Falling Bodies #3
WS -
Calculating Force Components
WS -
Charged Projectiles in Uniform Electric Fields
WS -
Combining Kinematics and Dynamics
WS -
Distinguishing 2nd and 3rd Law Forces
WS -
Force vs Displacement Graphs
WS -
Freebody Diagrams #1
WS -
Freebody Diagrams #2
WS -
Freebody Diagrams #3
WS -
Freebody Diagrams #4
WS -
Introduction to Springs
WS -
Kepler's Laws: Worksheet #1
WS -
Kepler's Laws: Worksheet #2
WS -
Kinematics Along With Work/Energy
WS -
Lab Discussion: Gravitational Field Strength and the Acceleration Due to Gravity
WS -
Lab Discussion: Inertial and Gravitational Mass
WS -
net F = ma
WS -
Parallel Reading - The Atom
WS -
Practice: Vertical Circular Motion
WS -
Ropes and Pulleys in Static Equilibrium
WS -
Standard Model: Particles and Forces
WS -
Static Springs: The Basics
WS -
Universal Gravitation and Satellites
WS -
Vocabulary for Newton's Laws
WS -
Work and Energy Practice: Forces at Angles
TB -
Systems of Bodies (including pulleys)
TB -
Work, Power, Kinetic Energy
Paul G. Hewitt
Copyright © 1984-2005
All rights reserved.
Used with written
permission.
PhysicsLAB
HTML conversion
Copyright © 1997-2018
Catharine H. Colwell
All rights reserved.
Mainland High School
Daytona Beach, FL 32114