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Name__________________________________ J#______
GPE, KE, Work, Momentum, Projectile Motion, Centripetal Force, and G-force
You will complete the following Centers in numerical order. Each center contains a Web Quest, and some
contain explorations. First, you will need to go to www.mrs-twedt.com on your computer. Follow the links
to “Coaster Centers.” Here, you will find a page that looks just like this sheet. Always start at the beginning
of each center and follow the questions in order. Click on the underlined words on Mrs. Twedt’s page in
order to get to the website that contains the answers! This time though, some centers will ask that you use
ScienceSaurus instead of the computer!!! Way to go! Be resourceful! 
Center 1: GPE (Gravitational Potential Energy) and Kinetic Energy
First, let’s review:
What is the difference between kinetic and potential energy? Yes….you know this, so let’s put it to use for
our project! Explain it in terms of a roller coaster. (Read from the beginning, be sure to watch the
animation, and make sure you include where the tracks come in to answer this!).
The animation above, “which demonstrates how a roller coaster's energy is constantly changing between
potential and kinetic energy. At the top of the first lift hill (a), there is maximum potential energy because the
train is as high as it gets. As the train starts down the hill, this potential energy is converted into kinetic
energy -- the train speeds up. At the bottom of the hill (b), there is maximum kinetic energy and little
potential energy. The kinetic energy propels the train up the second hill (c), building up the potential-energy
level. As the train enters the loop-the-loop (d), it has a lot of kinetic energy and not much potential energy.
The potential-energy level builds as the train speeds to the top of the loop (e), but it is soon converted back to
kinetic energy as the train leaves the loop.”
You are familiar with both of these: Gravitational Potential Energy and Kinetic Energy.
According to the text written below the heading “Gravitational Potential Energy” on this page, Gravitational
Potential Energy is
the energy stored in an object as the result of its vertical position or height. The energy is stored as the result
of the gravitational attraction of the Earth for the object.
Use that same page to fill in the following blanks: “The gravitational potential energy of the massive ball of
a demolition machine is dependent on two variables the mass of the ball and the height to which it is raised.
There is a direct relation between Gravitational Potential Energy and the Mass of an object; more massive
objects have greater gravitational potential energy. There is also a direct relation between Gravitational
Potential Energy and the Height of an Object; the More that an object is elevated, the greater the GPE.
These relationships are expressed by the following equation:”
PEgrav = mass • g • height
PEgrav = m *• g • h
Another way to look at this is Potential Energy (unit is Joules) = Weight x Height…… (since Mass x g (9.8)
= weight).
*Continue reading and scroll down to the “Quick Quiz” with the stairs and make sure you can calculate!
Kinetic Energy—Read the paragraph beginning with Kinetic Energy is the energy of motion. What is the
formula used to represent Kinetic Energy?
*What are the variables that determine the amount of kinetic energy? (explain what the letters above stand
for!).
m = mass of object
v = speed of object
What is their relationship? *Meaning, explain the equation. I’ll start you… For every twofold increase in
speed, the kinetic energy will increase by a factor of four. For a threefold increase in speed, the kinetic
energy will increase by a factor of nine. And for a fourfold increase in speed, the kinetic energy will increase
by a factor of sixteen. The kinetic energy is dependent upon the square of the speed.
SO, do you understand?
Prove it. I have a marble with a mass of .0032 kg. It rolls down a ramp at a
speed of 2.4 m/s. How much kinetic energy does my marble possess? Show your work. Include your unit!
KE = (.5) x (.0032 kg) x (2.4 m/s)2
.0092 J
Is Kinetic Energy a scalar quantity or a vector quantity? Kinetic energy is a scalar quantity; it does not have
a direction. Unlike velocity, acceleration, force, and momentum, the kinetic energy of an object is
completely described by magnitude alone.
Center 2: Work
Yes yes yes….I know…this is hard work. However, scientists don’t consider this work at all! Look up the
definition of work in the ScienceSaurus glossary. Then go to the page in the book where work is
discussed….
Work = when force is used to move an object through a distance
On the page where work is discussed more thoroughly, what is the formula that is used to find work? Please
write out each word. Do not just write letters.
Formula = Work
= Force x Distance
Read the example about the box that doesn’t move (in the center of the page). Using prior knowledge,
explain why the box doesn’t move! Think about Newton’s Laws!!!
The forces of gravity and friction are balanced against the push!
Thus, no work is able to be completed (Forces are balanced and no
distance is covered).
Exploration:
1. Attach the spring scale to the string tied around the book.
2. Using the spring scale and a meter stick, lift the book 1 meter off the ground or table. Make sure the
book is exactly 1 meter off the floor or table.
3. Record the amount of force shown on the spring scale. (You did this earlier this week and thought of
force as weight! This is still true!)
4. Calculate the amount of WORK that was done in Joules using the formula above and record.
5. Using the spring scale, pull (drag) the book across the floor for exactly 1 meter at a constant velocity.
6. Record the amount of force shown on the spring scale.
7. Calculate the amount of WORK that was done in Joules using the formula above and record.
Book when lifted 2 meters
Book when pulled across table 2 meters at a constant
velocity
Force (Newtons)
11N
2.4 N
Work (Joules)
22 J
4.8 J
Based on your calculations, does it require more work to lift an object or to drag it? LIFT! Because you have
to go against the force of gravity (making it FEEL like it weighs more).
Center 3: Momentum
According to the first cartoon, Momentum is “Mass
in Motion.”
Read the paragraph next to the first cartoon. Fill in the blanks below.
“All objects have Mass, so if an object is Moving then it has momentum - it has its mass in motion.
The amount of momentum which an object has is dependent upon two variables: how
moving
Mass
and
how fast the stuff is moving.
much stuff is
Momentum depends upon the variables
and Velocity.
Momentum = Mass x Velocity
Calculate:
1. Find the momentum of a 10-Kg object moving at 20 m/s.
200 kg-m/s
2. Determine the momentum of a ...
60-kg halfback moving eastward at 9 m/s.
60 x 9 = 540 kg-m/s east
1000-kg car moving northward at 20 m/s.
1000 x 20 = 20,000 kg-m/s north
40-kg 6th grader moving southward at 2 m/s. 40
x 2 = 80 kg-m/s south
3. A halfback (m = 60 kg), a tight end (m = 90 kg), and a lineman (m = 120 kg) are running down the
football field. Consider their ticker tape patterns below. (click ticker tape if you are unsure what it means).
Compare the velocities of these three players. How many times greater is the velocity of the halfback and the
velocity of the tight end than the velocity of the lineman?
Tight End = 6 m/s (twice the distance in the same amount of time, so
twice the speed)
Halfback = 9 m/s (three times the distance in the same amount of
time, so three times the speed)
Halfback and Tight end have the same momentum
60 x 9 = 540 kg-m/s
90 x 6 = 540 kg-m/s
The Lineman only has a momentum of 360 kg-m/s (120 x 3)
Center 4: Projectile Motion
Click on to this site:
BE sure to read the whole page, or you will be lost!
Projectiles, when launched follow a curved path (also known as trajectory).
Who can we credit for being the first to accurately describe projectile motion? Galileo
He stated that a projectile is actually influenced by TWO motions. What are they?
Horizontal and Vertical—
“a projectile is not only influenced by one motion, but by two. The motion that acts vertically is the
force of gravity, and this pulls an object towards the earth at 9.8 meters per second. But while gravity
is pulling the object down, the projectile is also moving forward, horizontally at the same time. And
this horizontal motion is uniform and constant according to Galileo's principle of inertia. He was
indeed able to show that a projectile is controlled by two independent motions, and these work
together to create a precise mathematical curve. He actually found that the curve has an exact
mathematical shape. A shape that the Greeks had already studied and called the parabola.”
Follow the next link at the bottom of that page.
Using your supplies at the table, carefully stand on a chair and drop the tennis ball and the bouncy ball (from
the exact same height). What happens?
They both hit at the same time.
Why? Due to the small size of the tennis ball and bouncy ball, when dropped, terminal velocity is reached so
the acceleration of gravity is constant (as gravity and drag are balanced).
Now, take two tennis balls. Drop one straight down at the same time that you toss the other at a slightly
projected angle. What happens? They hit at the same time.
Why? Two objects, the same size (and shape), will hit at the same time when dropped from the same height
even if the projection angle is different because the pull (acceleration) of GRAVITY is always the same.
Click this link. Run the simulator and launch various objects to hit a target. Read the directions. Adjust the
angles to prove that you can figure out projectile motion! Keep in mind, for your roller coaster, projectile
motion is important if you are planning on launching your marble. You must be very precise with your angle
to make sure you stay on track!
Center 5: Centripetal Acceleration (Force)
The force that causes objects to move in a circular path.
Give an example: The
moon revolves, or circles, the earth. Gravity between
the moon and earth, provides that centripetal force (along with the
acceleration of the orbit) that pulls the moon towards the center of
the earth.
Compare Centripetal Force to the parts of a car….which part is it most like? Seat Belt
Why? When
a roller coaster is going around a loop it will hold
passengers in their seats. It also helps to keep the train moving in a
circular track.
For roller coasters, what would happen if centripetal force did not exist in a loop? Make sure you READ.
Inertia keeps an object moving in a straight line (same
direction/speed) unless a different force stops it from doing that.
The track uses inertia to control the train. If centripetal force
didn’t exist in a loop, inertia might keep a train moving in a straight
line right off the track. Fortunately inertia and the track both do
their jobs.
Exploration:
Place the small pieces in the bucket.
CAREFULLY, swing the bucket in a wide circle making sure it is completely upside down at some point.
Your goal is to find the speed at which to swing the bucket allowing NOTHING to fall out.
Why doesn’t anything fall out? Centripetal Force. Think about your roller coaster…that is the force that
allows the coaster designers to build coasters with barrel rolls and corkscrews!
Explain, from prior knowledge, how Centripetal acceleration is truly a force. Think back (or look back) to
your Fusion packet where we discussed centripetal acceleration.
As an object spins around another object (center), it constantly accelerates (changing direction, not
necessarily speed), a force is created to counter any opposing force.
Center 6: G-Force
Remember in the video we just watched, it was explained that G-Force is when upwards acceleration is not
balanced with the downward force of gravity? Well, have you ever been on a roller coaster, or even a
swing, and at a certain point “felt light?” SO, do G Forces make you feel heavy or light? BOTH!!!!
Click HERE and scroll all the way down to G Forces (although, all the info above where you are about to
read is really good!). Explain the differences between positive and negative Gs.
Positive G-Force occurs at the bottom of a drop as the train wants to continue moving in one direction, but
the track is forcing it into the opposite direction. This can happen when pulling up at the bottom of a drop, or
when going around a banked corner. The sharpness of this change from going down to going up determines
the positive G.
Negative G is found at the top of hills and occurs when a train crests a hill at speed, or suddenly dips sharply
downwards. Negative G is the most fun G-Force, but it is also the most dangerous. The G forces between 0
and 1 (but less than 1) G's are also often considered negative-G's. This is because at anything less than 1G,
your body will experience a slight variation of the "floating" sensation you feel when you experience actual
negative G's.
On earth, simply standing, how much G-force are we normally feeling?
1G
What is this in terms of
acceleration? 9.8 m/s2 Does this look familiar??? G –Force is the force of gravity. When we worked
with weight (as a force), F = Mass x Acceleration OR Weight = Mass x 9.8 m/s2
Food for thought and clarification.--- When a sky diver jumps out of a plane and does not deploy his/her
parachute, s/he will eventually reach Terminal Velocity (where the force of gravity is balanced by the air
resistance or drag). At this point, the diver goes into Free Fall and experiences 0 Gs. Technically, s/he
should feel weightless, but the drag from the air (though balanced) feels like a small cushion of air!
Draw a rollercoaster track below with at least 1 hill and 1 loop. Label where you think a person on the
coaster would experience NEGATIVE Gs and POSITIVE Gs.
Let’s look at loops. Read the paragraph above the animation and study the animation. What are the only 2
forces acting on the actual person on a roller coaster? Gravity and Normal force from cart.
If they were equal, that would be a pretty boring rollercoaster. Think about it. Watch the animation.
* If I were to tell you that in a shuttle launch, that you will experience more than 2 Gs what will this mean
about your weight? You would feel HEAVY!!
Explain WHY you feel
this way. What does this mean about the force of gravity vs. what?
Your WEIGHT (mass x gravity) is accelerating against the force of gravity!
Things to work on when finished:
1. BrainPops—Force, Gravity, Acceleration, Newton’s 3 Laws, Work, Distance Rate and Time
2. Play the Coaster Creator on BrainPop-- http://www.brainpop.com/games/coastercreator/
3. Go to the simulator you found in projectile motion. Work with the other simulators you would find
useful in your roller coaster design process!