Slide 2 Slide 3 Slide 4 Slide 5 A roller coaster is called a
roller coaster because coasting is what it does, after it starts it
continues coasting throughout the track. Many of the calculations
rely on velocity in one way or another. Velocity is speed in a
given direction. In order to know an objects velocity, you must
know the speed and direction in which the object is traveling. To
find velocity, you divide distance by time ( V=d/t ) The velocity
is used to find acceleration. Which is the change in velocity
divided by change in time. Slide 6 Kinetic means to move and energy
means the ability to move Thus kinetic energy is the energy of
motion. For example the faster the object moves the more kinetic
energy is produced. The greater the speed and mass of an object the
more kinetic energy there will be! Slide 7 Potential Energy is the
same as stored energy. It is the energy of position. The greater
the height the greater the potential energy. The stored energy is
held within the gravitational field. For example, a lift motor,
from a roller coaster, exerts kinetic energy when lifting the cart
to the top of the hill as the cart moves up the hill the potential
energy increases. At the top of the hill the cart has a huge amount
of potential energy. As the cart is being dropped, the potential
energy decreases, and kinetic energy is gained. Slide 8 Roller
coasters operate because of conservation of energy ET = KE + PE
Mechanical energy (ET) on a roller coaster comes in two forms. KE=
Kinetic energy (1/2 mv 2 ) PE= Potential energy (mgh) To find the
total energy you add the potential and kinetic energies together at
the beginning of the ride. If we ignore friction than that is the
total energy found at any location on the track. Slide 9
Solution:ET(top of 1 st hill)= ET(top of 2 nd hill) (KE + PE) hill
1 = (KE + PE) hill 2 [(1/2)mv 2 + mgh] hill 1 = [(1/2)mv 2 + mgh ]
hill 2 the masses cancel because it is the same throughout the ride
[(1/2)v 2 + gh] hill 1 = [(1/2)v 2 + gh] hill 2 substitute the
numbers at each location (1/2)(.88) 2 + 9.8(.95) = (1/2)v 2 +
9.8(.65) notice all the numbers on the left side come from the top
of the 1 st hill while all the numbers on the right side come form
the top of the 2 nd hill.7744+ 9.31 = (1/2)v 2 + 6.37 3.7144 =
(1/2)v 2 7.4288 = v 2 v= 2.73 M/s . At the top of the 2 nd hill
Slide 10 Slide 11 Slide 12 Slide 13 Now Lets Do Some Math! Slide 14
Height at the top of our coaster- 47cm=.47m Height at the lowest
point of our coaster- 3.5cm=.035m Mass=55g Initial velocity=0 m/s
(velocity at top) (KE + PE) top = (KE + PE) bottom [(1/2)mv 2 +
mgh] top =[(1/2)mv 2 + mgh] bottom Slide 15 Velocity 1/2(55g)(0) 2
+(55g)(9.8m/s 2 )(.47m) = 1/2(55g)(v) 2 +(55g)(9.8m/s 2 )(.035m)
CALCULATING Slide 16 Velocity= 2.92m/s Slide 17 Slide 18 Free-fall
rides are really made up of three distinct parts: the ride to the
top, the momentary suspension, and the downward plunge. Slide 19
Galileo first introduced the concept of free fall. His classic
experiments led to the finding that all objects free fall at the
same rate, regardless of their mass. According to legend, Galileo
dropped balls of different mass from the Leaning Tower of Pisa to
help support his ideas. Slide 20 The speed at which an object is
falling during free fall can be determined, when started at rest,
by this equation: V=g* t or velocity=acceleration of gravity x the
change of time. The distance an object has traveled vertically
during free fall can be determined, when started at rest, by this
equation: D=1/2 g t 2 vertical distance= 1/2g (time) 2. Since
horizontal distance is independent from vertical distance we can
say the horizontal distance =vt Slide 21 We will assume the cart
starts at the top of the hill at a velocity of 7 m/s The exciting
hill is 100 meters tall Graphing the ordered pair as following
(Horizontal distance, vertical distance)or (vt,.5gt 2 ) This means
that for the 1 st second the cart will fall 4.9 meters. (7,4.9) At
2 seconds (14, 19.6); at 3 seconds (21,44.1) etc Slide 22 (Meters)
This is the Free Fall of an object traveling at an initial speed of
7 meters per second!!!!!!!!! Slide 23 Notice the shape of the graph
To increase the thrill of the ride, roller coaster designers often
make the track follow the same shape as the graph. This makes the
riders feel like they are free falling. Slide 24 Roller coasters
like this one, on the left, use steep drops to build up tremendous
speeds quickly, giving the rider the feeling of free fall. Slide 25
In the beginning of the ride, force is applied to the car to pull
it to the top of the first big hill. The amount of force that must
be applied depends on the mass of the car and its passengers. The
force is applied by motors, and there is a built-in safety
allowance. So the beginning is not the most thrilling.. Slide 26
The car is attached to this track, which gradually curves toward
the ground. A stretch of straight track allows the car to slow down
and brake, producing a controlled stop at the bottom, that keeps
passengers from getting injured. So you cant have the most
thrilling part of your roller coaster at the end So where does the
most thrilling part of the ride occur The top of the first hill.
Slide 27 As the car pulls it self to the highest point of the
roller coaster, it suddenly drops and begins to accelerate toward
the ground under the influence of the earth's gravity. The plunge
seems dramatic. Just as Galileo and Newton explain in their
theories of free fall, the least massive and most massive riders
fall to the earth with the same rate of acceleration. Slide 28 The
reason the most thrilling part is at the top of the roller coasters
first hill is because that is the highest point you will be
throughout the whole ride. Once you come racing down the big hill
at the top you are going so fast that you dont realize you are only
a few feet from the ground. Therefore, the most thrilling part of
the roller coaster is right when you hit the top of the first hill.
Slide 29 And dont forget to throw your hands up when you get to the
top Slide 30 Loops. Slide 31 Slide 32 Centripetal Acceleration V/r
gives you centripetal acceleration. Slide 33 Circular vs. Clothoid
Loops Clothoid LoopCircular Loops Slide 34 Notice as the roller
coaster enters the loop it has a radius of 15 meters. At the top of
the loop it has a radius of 5 meters. Then as the roller coaster
exits the loop it has a radius of 20 meters. Since the centripetal
acceleration is A=v 2 /r, the smaller the radius the more the
acceleration. This makes it possible to make it around the loop at
a smaller initial velocity. Clothoid loop 15 m 20m 5m Slide 35 The
Ninja Weasel Slide 36 Which loops have greater thrills? Clothoid or
circular loops? Clothoid loops are used on the Ninja Weasel because
they require a smaller velocity than circular loops. At the top of
the loop the radius is smaller this means the accelerations is
greater than it would be for a circular loop. Slide 37 Slide 38
Slide 39 Warning: G s can Kill!!! Force of one (uno) of Earths
atmospheric pressures. Amusement parks focus on getting roller
coasters to produce the maxim amount of Gs while staying in the
safe zone. Amusement parks focus on getting roller coasters to
produce the maxim amount of Gs while staying in the safe zone. The
safe zone for even high G rollercoaster is between 3.5 to 6.3 gs
The safe zone for even high G rollercoaster is between 3.5 to 6.3
gs Slide 40 The highest amount of Gs ever survived by a human being
was by John Stapp. The highest amount of Gs ever survived by a
human being was by John Stapp. He survived a G force of 46.2 times
the force of gravity for a little less than a second. He survived a
G force of 46.2 times the force of gravity for a little less than a
second. Remember exposure for more than a minute to 25+ Gs will
leave life long bodily injury and even death. Remember exposure for
more than a minute to 25+ Gs will leave life long bodily injury and
even death. G-Facts Slide 41 Formula for finding Gs A/9.8m/s 2
Centripetal Acceleration divided by 9.8 meters per second squared
For centripetal equations subtract one G from the top or add one to
the bottom. Example equation: Slide 42 Example equation We have a
random rollercoaster at the top of a traditional loop. We know
gravity and are going to use a random acceleration of (55 m/s 2 ).
Notice the gs felt change according to your position on the roller
coaster(top or bottom of the loop). Slide 43 On the top to the loop
you subtract 1 g from the number of gs calculated Slide 44
