Worksheet
Advanced Properties of Freely Falling Bodies #1
Printer Friendly Version
As we continue our study of freely-falling bodies, there are further properties that we should understand to more fully describe a projectile's behavior.
In addition to its kinematics properties of how fast (velocities), how far (heights and displacements), how long (time) there are the properties of momentum, potential energy, and kinetic energy. Moreover, we are often asked how much work did gravity do on an object during the object's trajectory.
Momentum
is a vector quantity calculated as the product of the object's mass times its velocity. The direction of the momentum vector agrees with the direction of the object's velocity.
The formula to calculate momentum is:
p
= m
v
.
Momentum is measured with the units of kg m/sec.
Potential energy
is a measure of the stored energy an object acquires by virtue of its position in a gravitational field. Potential energy is calculated as the product of an object's mass times the local gravitational field strength times the object's height above an arbitrarily chosen zero position. Potential energy is a scalar quantity.
The formula to calculate potential energy is: PE
g
= mgh.
Potential energy has units of kg(m/sec
2
)(m) = kg m
2
/sec
2
= Joules
Kinetic energy
is a measure of the energy acquired by an object due to its motion. Kinetic energy is also a scalar - that is, it only has magnitude, not direction. Kinetic energy is calculated as ½ of the product of the object's mass times the square of the object's velocity.
The formula to calculate kinetic energy is: KE = ½mv
2
.
Kinetic energy has units of kg (m/sec)
2
= kg m
2
/sec
2
= Joules
Work
is yet another scalar quantity. The work done on an object is defined as the product of the applied force which is parallel (or anti-parallel) to the direction of motion times the distance through which the object is moved. The work done on an object is also defined as the change in an object's kinetic energy. There are two formulas to calculate work.
These formulas are: W = F
||
d and W = KE
f
- KE
o
.
Work is also measured in Joules.
When the work done on an object is positive, the object has gained speed and therefore KE. Negative work means that the object has slowed down and lost KE.
A
freebody diagram (FBD)
is a diagram summarizing only the forces acting on the object. In this unit on freely-falling bodies, we will examine two forces: weight and normals. We have already covered
weight
(the force of gravitational attraction between the mass and the mass of the planet). A
normal force
is a force supplied by a supporting surface. This force can be supplied by someone's hand holding a projectile, a table and the floor/ground.
The weight vector is always drawn by starting at the object's center of mass and pointing straight to the center of the earth/planet. The normal is always drawn perpendicular to the plane of the supporting surface and also passes through the center of mass. When an object is in
equilibrium
these two vectors will have exactly the same magnitude, or length. This would occur if the object were at rest or moving at a constant velocity (no acceleration). If an
unbalanced force
acts on the object (for example, only one force) then the object will be accelerated in the direction of that unbalaced force. An example of this situation would be a projectile in freefall.
Refer to the following information for the next six questions.
A 24.5 N ball is held at rest 10 meters above the surface of the earth.
Find the values of the following givens stated in the problem:
1(a). Height (h) = _______ m
1(b). Weight (Wt) = _______ N
2. Draw a freebody diagram (FBD) of the forces acting on the ball while it is being held at rest in your hand.
3. What is the gravitational field strength of the earth at the ball’s location given that the mass of the earth is 6.0 x 10
24
kg and the earth’s average radius is 6.4 x 10
6
meters?
4. What is the mass of the ball?
5. How much potential energy does the ball have, relative to the ground, while it is being held 10 meters above the earth's surface?
Refer to the following information for the next ten questions.
To release the ball your hand is gently removed thus allowing the ball to fall to the earth from a state of rest.
Find the values of the following givens stated in the problem.
6(a). Initial velocity (v
o
) = _______ m/sec
6(b) Displacement (s) = _______ m
7. Draw a FBD of the ball while it is falling if the force of gravitational attraction of the earth is the only force acting on the ball.
8. Based on your answer to
Question 3
, what acceleration will the ball experience as it falls to the earth’s surface?
9. What is the ball’s velocity just as it strikes the ground?
10. How much time did it take the ball to reach the ground?
11. If a 4.9 N brick had been dropped from rest instead of the ball, would the brick require more, less, or the same amount of time to reach the ground? Support your choice.
more time
less time
the same amount of time
12. How much momentum will the ball have just as it strikes the ground?
13. How much kinetic energy will the ball have just as it strikes the ground?
14. How much work did gravity do
on the ball
as the ball was pulled to the earth’s surface?
Related Documents
Lab:
Labs -
A Battering Ram
Labs -
A Photoelectric Effect Analogy
Labs -
Acceleration Down an Inclined Plane
Labs -
Air Track Collisions
Labs -
Ballistic Pendulum
Labs -
Ballistic Pendulum: Muzzle Velocity
Labs -
Bouncing Steel Spheres
Labs -
Coefficient of Friction
Labs -
Coefficient of Friction
Labs -
Coefficient of Kinetic Friction (pulley, incline, block)
Labs -
Collision Pendulum: Muzzle Velocity
Labs -
Conservation of Energy and Vertical Circles
Labs -
Conservation of Momentum
Labs -
Conservation of Momentum in Two-Dimensions
Labs -
Cookie Sale Problem
Labs -
Falling Coffee Filters
Labs -
Flow Rates
Labs -
Force Table - Force Vectors in Equilibrium
Labs -
Freefall Mini-Lab: Reaction Times
Labs -
Freefall: Timing a Bouncing Ball
Labs -
Galileo Ramps
Labs -
Gravitational Field Strength
Labs -
Home to School
Labs -
Impulse
Labs -
Inelastic Collision - Velocity of a Softball
Labs -
Inertial Mass
Labs -
InterState Map
Labs -
LAB: Ramps - Accelerated Motion
Labs -
LabPro: Newton's 2nd Law
Labs -
LabPro: Uniformly Accelerated Motion
Labs -
Loop-the-Loop
Labs -
Mass of a Rolling Cart
Labs -
Moment of Inertia of a Bicycle Wheel
Labs -
Monkey and the Hunter Animation
Labs -
Monkey and the Hunter Screen Captures
Labs -
Projectiles Released at an Angle
Labs -
Ramps: Sliding vs Rolling
Labs -
Range of a Projectile
Labs -
Relationship Between Tension in a String and Wave Speed
Labs -
Relationship Between Tension in a String and Wave Speed Along the String
Labs -
Roller Coaster, Projectile Motion, and Energy
Labs -
Rotational Inertia
Labs -
Rube Goldberg Challenge
Labs -
Spring Carts
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 -
Target Lab: Ball Bearing Rolling Down an Inclined Plane
Labs -
Terminal Velocity
Labs -
Video LAB: A Gravitron
Labs -
Video Lab: Ball Bouncing Across a Stage
Labs -
Video LAB: Ball Re-Bounding From a Wall
Labs -
Video Lab: Blowdart Colliding with Cart
Labs -
Video Lab: Cart Push #2 and #3
Labs -
Video LAB: Circular Motion
Labs -
Video Lab: Falling Coffee Filters
Labs -
Video Lab: M&M Collides with Pop Can
Labs -
Video Lab: Marble Collides with Ballistic Pendulum
Labs -
Video Lab: Two-Dimensional Projectile Motion
Resource Lesson:
RL -
A Further Look at Impulse
RL -
Accelerated Motion: A Data Analysis Approach
RL -
Accelerated Motion: Velocity-Time Graphs
RL -
Advanced Gravitational Forces
RL -
Air Resistance
RL -
Air Resistance: Terminal Velocity
RL -
Analyzing SVA Graph Combinations
RL -
APC: Work Notation
RL -
Average Velocity - A Calculus Approach
RL -
Chase Problems
RL -
Chase Problems: Projectiles
RL -
Comparing Constant Velocity Graphs of Position-Time & Velocity-Time
RL -
Conservation of Energy and Springs
RL -
Constant Velocity: Position-Time Graphs
RL -
Constant Velocity: Velocity-Time Graphs
RL -
Derivation of the Kinematics Equations for Uniformly Accelerated Motion
RL -
Derivatives: Instantaneous vs Average Velocities
RL -
Directions: Flash Cards
RL -
Energy Conservation in Simple Pendulums
RL -
Famous Discoveries: The Franck-Hertz Experiment
RL -
Forces Acting at an Angle
RL -
Freebody Diagrams
RL -
Freefall: Horizontally Released Projectiles (2D-Motion)
RL -
Freefall: Projectiles in 1-Dimension
RL -
Freefall: Projectiles Released at an Angle (2D-Motion)
RL -
Gravitational Energy Wells
RL -
Inclined Planes
RL -
Inertial vs Gravitational Mass
RL -
Linear Momentum
RL -
Mechanical Energy
RL -
Momentum and Energy
RL -
Monkey and the Hunter
RL -
Newton's Laws of Motion
RL -
Non-constant Resistance Forces
RL -
Potential Energy Functions
RL -
Principal of Least Action
RL -
Properties of Friction
RL -
Rotational Dynamics: Pivoting Rods
RL -
Rotational Kinetic Energy
RL -
Springs and Blocks
RL -
Springs: Hooke's Law
RL -
Static Equilibrium
RL -
Summary: Graph Shapes for Constant Velocity
RL -
Summary: Graph Shapes for Uniformly Accelerated Motion
RL -
SVA: Slopes and Area Relationships
RL -
Symmetries in Physics
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 -
Vector Resultants: Average Velocity
RL -
What is Mass?
RL -
Work
RL -
Work and Energy
Review:
REV -
Test #1: APC Review Sheet
Worksheet:
APP -
Big Fist
APP -
Family Reunion
APP -
Hackensack
APP -
Puppy Love
APP -
The Antelope
APP -
The Baseball Game
APP -
The Big Mac
APP -
The Box Seat
APP -
The Cemetary
APP -
The Golf Game
APP -
The Jogger
APP -
The Pepsi Challenge
APP -
The Pet Rock
APP -
The Pool Game
APP -
The Raft
APP -
The Spring Phling
CP -
2D Projectiles
CP -
Action-Reaction #1
CP -
Action-Reaction #2
CP -
Conservation of Energy
CP -
Conservation of Momentum
CP -
Dropped From Rest
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 -
Freefall
CP -
Gravitational Interactions
CP -
Incline Places: Force Vector Resultants
CP -
Incline Planes - Force Vector Components
CP -
Inertia
CP -
Mobiles: Rotational Equilibrium
CP -
Momentum
CP -
Momentum and Energy
CP -
Momentum and Kinetic Energy
CP -
Momentum Practice Problems
CP -
Momentum Systems and Conservation
CP -
Net Force
CP -
Newton's Law of Motion: Friction
CP -
Non-Accelerated and Accelerated Motion
CP -
Power Production
CP -
Satellites: Circular and Elliptical
CP -
Static Equilibrium
CP -
Tensions and Equilibrium
CP -
Tossed Ball
CP -
Up and Down
CP -
Work and Energy
NT -
Acceleration
NT -
Air Resistance #1
NT -
An Apple on a Table
NT -
Apex #1
NT -
Apex #2
NT -
Average Speed
NT -
Back-and-Forth
NT -
Cliffs
NT -
Crosswinds
NT -
Elliptical Orbits
NT -
Escape Velocity
NT -
Falling Rock
NT -
Falling Spheres
NT -
Friction
NT -
Frictionless Pulley
NT -
Gravitation #1
NT -
Gravitation #2
NT -
Head-on Collisions #1
NT -
Head-on Collisions #2
NT -
Headwinds
NT -
Ice Boat
NT -
Momentum
NT -
Monkey Shooter
NT -
Pendulum
NT -
Projectile
NT -
Ramps
NT -
Rotating Disk
NT -
Sailboats #1
NT -
Sailboats #2
NT -
Satellite Positions
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 -
Accelerated Motion: Analyzing Velocity-Time Graphs
WS -
Accelerated Motion: Graph Shape Patterns
WS -
Accelerated Motion: Practice with Data Analysis
WS -
Advanced Properties of Freely Falling Bodies #2
WS -
Advanced Properties of Freely Falling Bodies #3
WS -
Average Speed and Average Velocity
WS -
Average Speed Drill
WS -
Calculating Force Components
WS -
Charged Projectiles in Uniform Electric Fields
WS -
Chase Problems #1
WS -
Chase Problems #2
WS -
Chase Problems: Projectiles
WS -
Combining Kinematics and Dynamics
WS -
Constant Velocity: Converting Position and Velocity Graphs
WS -
Constant Velocity: Position-Time Graphs #1
WS -
Constant Velocity: Position-Time Graphs #2
WS -
Constant Velocity: Position-Time Graphs #3
WS -
Constant Velocity: Velocity-Time Graphs #1
WS -
Constant Velocity: Velocity-Time Graphs #2
WS -
Constant Velocity: Velocity-Time Graphs #3
WS -
Converting s-t and v-t Graphs
WS -
Distinguishing 2nd and 3rd Law Forces
WS -
Energy Methods: More Practice with Projectiles
WS -
Energy Methods: Projectiles
WS -
Energy/Work Vocabulary
WS -
Force vs Displacement Graphs
WS -
Freebody Diagrams #1
WS -
Freebody Diagrams #2
WS -
Freebody Diagrams #3
WS -
Freebody Diagrams #4
WS -
Freefall #1
WS -
Freefall #2
WS -
Freefall #3
WS -
Freefall #3 (Honors)
WS -
Horizontally Released Projectiles #1
WS -
Horizontally Released Projectiles #2
WS -
Introduction to Springs
WS -
Kinematics Along With Work/Energy
WS -
Kinematics Equations #1
WS -
Kinematics Equations #2
WS -
Kinematics Equations #3: A Stop Light Story
WS -
Lab Discussion: Gravitational Field Strength and the Acceleration Due to Gravity
WS -
Lab Discussion: Inertial and Gravitational Mass
WS -
net F = ma
WS -
Position-Time Graph "Story" Combinations
WS -
Potential Energy Functions
WS -
Practice: Momentum and Energy #1
WS -
Practice: Momentum and Energy #2
WS -
Practice: Vertical Circular Motion
WS -
Projectiles Released at an Angle
WS -
Ropes and Pulleys in Static Equilibrium
WS -
Rotational Kinetic Energy
WS -
Standard Model: Particles and Forces
WS -
Static Springs: The Basics
WS -
SVA Relationships #1
WS -
SVA Relationships #2
WS -
SVA Relationships #3
WS -
SVA Relationships #4
WS -
SVA Relationships #5
WS -
Vocabulary for Newton's Laws
WS -
Work and Energy Practice: An Assortment of Situations
WS -
Work and Energy Practice: Forces at Angles
TB -
2A: Introduction to Motion
TB -
2B: Average Speed and Average Velocity
TB -
Antiderivatives and Kinematics Functions
TB -
Honors: Average Speed/Velocity
TB -
Kinematics Derivatives
TB -
Projectile Summary
TB -
Projectile Summary
TB -
Projectiles Mixed (Vertical and Horizontal Release)
TB -
Projectiles Released at an Angle
TB -
Set 3A: Projectiles
TB -
Systems of Bodies (including pulleys)
TB -
Work, Power, Kinetic Energy
PhysicsLAB
Copyright © 1997-2025
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton