GENERAL INFO PACKET!
The Study of Mechanics, Energy, Force & Motion
There are two basic types of motion. Motion that is uniform and accelerated
For an object moving with uniform motion, the velocity remains in the same
direction and has constant magnitude (size). For uniform motion, forces are
balanced. There are no net or resulting forces. Under these conditions calculating
the velocity is straightforward.
velocity = distance traveled = s or d
time of travel t
This velocity is an average for the trip.
As soon as forces that do not cancel each other out act on an object, uniform motion
no longer takes place. Whenever an unbalanced force acts on an object an
acceleration is produced. Newton’s second law of motion expresses the relationship
among force, mass, and acceleration as F = ma.
Force = mass x acceleration or acceleration = Force
The acceleration of an object increases as the amount of force causing the
acceleration increases. The larger the mass of the object, the larger the force
needed to produce acceleration.
Acceleration is the change in velocity over a period of time. (How fast something is
going faster.) This change can be in the speed (whether increasing or decreasing), in
the direction of the motion, or in both.
Acceleration = velocity / time a = v / t
Acceleration occurs anytime there is a change in velocity. For objects moving in a
curved path, velocity is changing even though speed may be constant. Velocity is a
vector and therefore must have speed and direction. If your direction is changing,
like on the Rotor, then there is acceleration toward the center of the Rotor. This
acceleration is called centripetal acceleration.
centripetal acceleration = (velocity)2 / divided by the radius
ac = centripetal acceleration
ac = v2 /r v = velocity
r = radius of the circle
In the case of an object spinning in a circle, the size of the velocity (speed) is
calculated by measuring the time for one complete spin and dividing this into
circumference of the circle.
v = Circumference / time
If there is an acceleration, there must be an unbalanced force producing it. The force
causing the circular motion is called centripetal force (Fc). This force causes the
object to change direction, thereby creating the acceleration in the same direction
(toward the center).
As stated previously;
F = ma
Newton’s Second Law of Motion must also apply to circular motion.
Therefore: Fc = mac
If we substitute ( v2 / r) in for (ac), we find the equation needed to calculate
Fc = mv2 / r
This force is easy to see and understand if you swing a rubber stopper on the end of
a string. You can see your hand is producing the force which is transferred through
the string to make the stopper follow the circular path. So your hand produces the
force, which causes the centripetal acceleration.
In the Rotor, the wall produces the centripetal force. This force keeps you moving in
a circular path by providing an acceleration on you toward the center. You, on the
other hand, have the impression that there is a force throwing you toward the wall.
This is very similar to being in an automobile at rest and the driver pushes the
accelerator to the floor. If the car has a lot of horsepower, you feel like you are being
pushed back in the seat. In reality, the seat is accelerating you forward. This “force”
you feel back against the seat does not really exist. It’s your inertia trying to keep
you at rest. The only force is the seat accelerating you. So, in the Rotor, the force
you feel out against the wall, called centrifugal force, is a fictitious force. You are
reacting to the wall pushing on you!
Generally speaking, you might think of centripetal force as an action force and
centrifugal force as a reaction force. Remember, centrifugal force is considered to be
fictitious. It can only be observed in the accelerated frame of reference.
These forces are also found on many other rides at Lake Compounce! Any ride which
moves in a circular or curved path will produce centripetal and centrifugal forces.
Earth Gravity and G - Forces
Gravity refers to the force of attraction between objects. All objects exert a
gravitational force. Any two objects with mass attract each other, and the strength
of this force depends on the mass of the objects and the distance between them.
The larger or more massive the object, the greater the force.
Some forces can act from a distance without actual contact between the two objects.
We are accustomed to the gravity of Earth. When you are standing still the force
exerted on you by the Earth produces your weight. This is also referred to as one “g”.
Gravity causes free-falling objects on the Earth to change their speeds at the rate of
9.8 m/s each second. That is a change in speed of 32 ft/s in each consecutive
second. Therefore, a “g” is a unit of acceleration equal to the acceleration caused by
gravity. When you feel heavier than normal you are experiencing a force greater
then 1 g. When you feel lighter than normal you are experiences a force less than
1 g. You are weightless when you feel no forces (free fall).
On the roller coaster, when you go down a steep hill, you will get that “light stomach
feeling” and will notice yourself lifting off the seat. You have just experienced
weightlessness. Imagine the shuttle astronauts having this same feeling continually
for several days. This may give you an idea of why many astronauts have what is
known as space or motion sickness. While the shuttle is in orbit, it is falling. With
its tremendous horizontal velocity, as it falls the Earth curves away from it. So it
never hits the Earth, it falls in an orbit.
G – Force Information:
Definition: The ratio produced when the force felt by an object is
divided by the force that the object would feel while
motionless on the Earth’s surface.
Examples of g- forces:
Shuttle in Orbit 0 g’s
The Moon .165 g’s
Mars .38 g’s
Shuttle Lift Off 3.0 g’s
Sun 28 g’s
There are many energy transformations that occur at Lake Compounce.
The main energies used to make calculations involve gravitational potential energy
and kinetic energy. Potential energy is energy that is stored. Kinetic energy is
energy of motion.
When an object is lifted from the ground or rest position it acquires potential energy.
The amount of energy can be expressed as:
Ep = mgh
where: m = mass (kg)
g = acceleration due to gravity (m/s2)
h = height above starting position (m)
Energy is measured in units called JOULES.
When the object drops, the potential energy that it has is changed to kinetic energy
as the object falls. At the bottom of its fall, the object is moving at its fastest velocity
which indicates it has its maximum kinetic energy. This kinetic energy can be
Ek = 1⁄2 mv2
where: m = mass (kg)
v = velocity (m/s)
Conversion of energy requires that the total potential at the top must be equal to the
total kinetic at the bottom. If you calculate the potential energy at the top and set it
equal to (1⁄2 mv2 )the maximum velocity at the bottom can be calculated.
Work & Power
Work is produced by a force acting on an object moving through a distance.
Work = Force x distance
W = Fd where: W = work (joules)
F = Force (newtons)
d = distance (meters)
Notice the unit for work (joules) is the same as the units of energy. Energy is the
ability to do work. If work is done to lift an object, that work reappears as potential
Power is the rate of doing work, or how fast work is done.
work W Fd
Power = time = t = t
Where; P = power (watts)
W = work (joules)
t = time (seconds)
Power in watts can be converted to horsepower using the following
1 hp = 746 watts
An Angle on Distance
To determine the height of a ride use a simple “protractor” elevation finder.
Have one student sight through the straw at the top of the ride.
Another student reads the angle on the protractor. The angle read
is then subtracted from 90 degrees.
To calculate the height of the ride you will also need the distance between the
student and the ride.
(Remember to add the height of your eye to the ground.)
1. Cut out the protractor including the dashed line section.
2. Trace the protractor part only on a piece of cardboard,
such as the back of a tablet.
3. Glue or staple the cardboard to the back of the paper protractor.
4. Roll the top section around a straw and tape.
5. Punch a hole and tie a 9 inch string of heavy black thread through
the hole. On the other end tie a metal nut, washer, or fish sinker.
6. Follow the directions on the page titled “An Angle on Distance.”
acceleration The rate at which velocity changes. This occurs if there is change in speed or direction.
centrifugal force A reaction force to centripetal force, which you feel in a moving frame. This is a fictitious force. When your body responds to an acceleration you think there is a force pushing you back.
centripetal force A force acting toward the center which makes objects turn.
circumference The distant around a circular object.
diameter The distance across a circle through the center.
force A push or pull.
frame or reference Where you are when you make an observation. (eg. Earth frame or moving frame)
friction A force which opposes motion between objects in contact.
g force A multiplication factor which compares a force to a person’s weight. (eg. 2 g’s is twice your weight)
gravity A force of attraction between objects.
horsepower A unit established for comparison to the power of a horse. (1 hp = 746 watts)
inertia A property of matter which resists a change in its current state of motion.
joule A unit of work and / or energy in the metric system
kilogram A unit of mass in the metric system. (1000 grams)
kinetic energy The energy of motion. The energy an object has due to its velocity. KE = 1/2mv2
mass The amount of matter an object contains. Mass is unaffected by a change in gravity.
meter The basic unit of length in the metric system.
momentum A measure of how lard it is to stop a moving object. (mass x velocity)
newton A unit of force in the metric system.
parabola A curved path of an object moving at right angles to a gravitational field.
potential energy Stored energy. The energy an object has due to its position.
Gravitational potential energy = weight x height
power The rate of doing work. (P = work / time)
projectile An object which has been given kinetic energy and is moving with no self propulsion.
protractor A measuring device which indicates angles in degrees.
radius The distance from the center of a circle out to the edge.
watt The unit of power in the metric system. 1 watt = 1 joule / sec.
weight The force with which an object is pulled toward the Earth; measurement of force of
weightlessness A condition in which you feel no forces acting on you.
work When a force acts on an object causing it to move through a distance. The amount of energy gained by an object that’s moved is equal to the work needed to move it (no friction). Work = Force x distance