Ocoee High School Physics Universal

Ocoee High School Physics and Engineering at
Universal: Islands of Adventure
Names:____________________________________
This trip will exclusively use smart phone applications and/or
functions. Here is what you will need:
•
•
•
•
Stopwatch app
Angle meter (phone can be angled to show degrees)
Colornote Notepad or other Note pad app
Video capability
Legend:
RP = Regular Physics
HP = Honors Physics
APB = AP Physics B
APC = AP Physics C
Note: Unlabeled questions are done by ALL LEVELS of physics
Roller Coaster
oaster Physics Analysis
1. How do you find the speed of a roller coaster at a specific point?
2. How do you find the lengths and radii of ride elements?
Since you are not bringing a meter stick to the park the best way is to measure
the length of your shoe. When measuring a distance we simply step the distance
out “heel-to-toe”
toe” then multiply the # of steps by the length of our shoe.
L total = l shoe *# of footsteps taken
3. How do I take proper video footage?
This is actually very simple
simple.. The single most important rule is that you MUST be
perpendicular to the ride element you want to capture. And you also should be
far enough away so that the element can enter the screen and leave the screen
but never take up the entire screen. You also need
eed to know the LENGTH of
the object you want to take video footage of
of.. So make sure you heel to toe
across
cross the length of the object if you do not know it.
4. How do I measure the angle of a ride?
Easy! Use the ANGLE METER app on the smart phone. Stand perpendicular
perp
to
the ride you want to measure with a good amount of distance between you and
the ride. Align the side edge of your phone with the ride and read the angle
reading off your phone.
5. How do I measure the time of a ride?
Use the stopwatch app on your phone.
6. How do I record data at the park?
Use a notepad app on your phone.
Caro-Seuss-el
What to measure in addition to the data
table below:
• Video of ride rotating
Note: The 2 chosen ride elements
element must be
clearly seen in
n the video. This is needed to
do the video analysis.
Data
Period of 3
revolutions
(sec)
Radius of
inner circle
(meters)
Radius of
outer circle
(meters)
3.51 m
6.78 m
Length of
inner ride
element
(meters)
Length of
outer ride
element
(meters)
Calculations - You MUST show all work and formulas used!!!
1. Using the period for 3 revolutions, calculate the period for ONE revolution.
2. Using the radius of the inner circle, calculate the velocity of the inner ride
element.
3. Using the radius of the outer circle, calculate the velocity of the outer ride
element.
4. Using Logger Pro’s Video analysis, determine the velocity (slope of
distance vs. time graph) of each ride element using the length of each
element.
Video Velocity of Inner Element
Video Velocity of Outer Element
5. Using your calculated and video velocity, determine a percent difference
between the values for each ride element.
%difference =
value1 − value 2
x100
average
Inner
Element
Outer
Element
6. On the figure shown, draw and label the vectors for
velocity, acceleration, and force of a ride element.
7. (APC) – Calculate the ANGULAR velocity of each ride element.
ωinner
ωouter
8. (APC) - Explain the significance regarding the values of the angular
velocity you calculated.
Jurassic Park: The Ride
What to measure in addition to the data table below.
• Video footage of boat moving after the splash
sp
Ride Specifications
Boat length = 7.5 m
Velocity of boat at the top of the drop = 3 m/s
Drop Height = 26 m
Data
Time of splash (this is the time it takes to slow the boat down to a constant speed)
Trial 1
Trial 2
Trial 3
Average
Calculations – You MUST show all work and formulas used!!!
1. Using conservation of energy, calculate the speed of the boat at the bottom
of the drop. Assume the boat is at ground level.
2. Using Logger Pro’s Video analysis, determine the velocity (slope of
distance vs. time graph) of the boat AFTER the splash. It should be moving
at a constant speed at this point.
Velocity of boat after splash =
3. Using kinematics, calculate the accelerat
acceleration
ion (deceleration) of the boat
during the splash.
4. Calculate the CHANGE in momentum of the boat if a fully loaded boat is
approximately 4500 kg.
5. Since the change in momentum is equal to the IMPULSE, determine the
average force that the water exerted on the boat during splash time
interval.
6. Acquire the force from at least 1 other group. Determine a % difference
between YOUR calculated force value and the force from the other group.
7. Is the percent difference off by more than 10%? If so, what factors could
account for this difference thinking about the ACTUAL situation at the park.
What to measure in addition to the data table below.
•
•
•
Video footage of hulk coaster leaving the launch tube
tube.
Video footage of hulk coaster traveling down the first drop. (APC
APC only)
only
Video footage of hulk coaster at the bottom of the first drop
drop.
Ride Specifications
Length of coaster = 13.1 m
Time of Launch = 2 seconds
Initial velocity of Hulk = 3 m/s
Height of zero g roll = 34 m
Height of lowest point after zero g roll = 2 m
Claimed final velocity of Hulk at end of launch tube = 17.9 m/s
Data
Time for coaster at a single position in the zero g roll after launch tube
Trial 1
Trial 2
Trial 3
Average
Time for coaster at a single position at the bottom of the first drop
Trial 1
Trial 2
Trial 3
Average
Angle of Descent after zero g roll =
(you need to be perpendicular to the ride to measure this)
Calculations -– You MUST show all work and formulas used!!!
1. Calculate the velocity of the coaster in the zero g roll if the length of the
coaster is 13.1 m.
2. Using Logger Pro’s Video analysis, determine the velocity (slope of
distance vs. time graph) of the coaster in the zero g roll.
Velocity of coaster in zero g roll (video) =
3. Calculate a % difference between the velocity you determined using the
video footage and the velocity you calculated in #1.
4. Using Logger Pro’s Video analysis, determine the velocity (slope of
distance vs. time graph) of the coaster at the BOTTOM of the first drop
Velocity of coaster at bottom of drop (video) =
5. (R,H,APB) Calculate the length of the drop
using your measured angle and the height
difference.
6. (R,H,APB) Using kinematics, calculate the acceleration of the incline.
7. (APC) Using Logger Pro
Pro’s
’s Video analysis and the video footage of the
coaster traveling down the first drop, create a distance time graph for the
entire descent. This graph should have a LOT of points! Take the derivative
of the position graph to get the velocity. Make a velocity time graph and
find the SLOPE, which is the acceleration of the coaster.
Acceleration of coaster from video =
8. On the figure below, draw the free body diagram of the coaster as it
descends the first drop. Assume that since the coaster is rolling that
friction is negligible.
9. In the box below, write the EQUATION OF MOTION in the direction the
coaster is moving as it descends the first drop. (R – You might need help
with this)
10. Using the equation above, show what the acceleration is equal to in terms.
Calculate the magnitude of the acceleration using your measured angle.
11. Calculate a % difference between the acceleration found in #10 and the
one you found in #6 (APC uses #7)
The Dragon Challenge:
Chinese Fireball vs.
Hungarian Horntail
What to measure in addition to the data
table below.
• Video footage of BOTH coasters
in small vertical loop.
Data Table
Time for coaster at a single position at top of small vertical loops
Chinese Fireball
Hungarian Horntail
Trial 1
Trial 2
Trial 3 Average Trial 1
Trial 2
Trial 3 Average
Calculations -– You MUST show all work and formulas used!!!
1. Calculate the velocity of EACH coaster using your average time and the
length of the coaster which is 11.6 m.
2. Calculate a % difference between the calculated velocity values in #1.
3. Using Logger Pro’s Video analysis, determine the velocity (slope of
distance vs. time graph) of EACH coaster at the TOP of the small
vertical loop.
Chinese Fireball’s velocity
Hungarian Horntail’s velocity
4. Calculate a % difference between the measured video velocity values in
#3.
5. The ride itself used to be dueling in nature in that there was a “near
miss” between the coasters. An accident has since forced park officials
to NOT coordinate the 2 coasters in this way. To ensure that the timing
was perfect the speeds had to be nearly identical. Is this the case?
Explain.
6. The vertical loops we just used are NOT perfect circles but they are in
fact “engineered” using circles. The figure shows what is called a
CLOTHOID loop. Two circles with the same radius are drawn in such a
way as they overlap. I third circle is drawn inside the area that the 2
original circles share. This idea builds the shape of the CLOTHOID
LOOP, where the top part of the clothoid will have the radius on the
smaller inscribed circle. On the second figure, draw the FREE BODY
DIAGRAM for the coaster when it is at the TOP of the LOOP.
7. In the box below, write the EQUATION OF MOTION for the coaster when
it is at the TOP of the coaster.
8. Is the acceleration of the coaster, LINEAR or CENTRIPETAL? (circle
one)
9. In the box below, write the complete EQUATION OF MOTION using your
answer to #8 and the appropriate symbolic expression for that answer.
10. Divide EACH term in your expression in #9 by WEIGHT (“mg”) and
reduce or simplify. Show this expression below.
11. The idea of “G-FORCE” is defined as the RATIO of the force normal to
the weight. You should see this ratio in your expression. Replace the
fraction with the term “g-force” and solve for it IN TERMS. Show the
expression for the g-force of a rollercoaster when it is upside down
below.
12. Using your derived expression in #11, calculate the g-force of the
Hungarian horntail if the radius of the clothoid loop at the top is 5.5 m.
13. Conceptually, the unit for g-force is “g”. The meaning behind this is
that if you experienced 5g’s that would translate to a feeling of FIVE
TIMES your mass or feeling 5 times heavier than normal. At rest we are
all at 1g. Consider the value you calculated in #12, would a rider feel
HEAVIER or LIGHTER at the top of the loop. EXPLAIN in detail.
14. A typical g-force measurement for a loop with this size radius is 2g.
Calculate a % difference between this measurement and your calculated
measurement in #12.
Flight of the
Hippogriff
Ride Specifications
Height of Lift above the loading platform = 12.1 meters
Mass of fully loaded coaster = 4500 kg
Data Table
Time for coaster to ascend the lift =
ANGLE of LIFT HILL =
Calculations -– You MUST show all work and formulas used!!!
1. Using your average time for the lift motor to pull the coaster up the lift
hill, calculate the POWER that the lift motor expends.
2.
Calculate the LENGTH of the lift hill
using the figure as a reference.
3. In the box below, calculate the CHANGE in POTENTIAL ENERGY of the
coaster as well as the WORK DONE BY THE LIFT CHAIN. Keep mind that
the lift chain pulls the coaster at a constant speed and is equal to a
component of the coaster weight.
Change in Potential Energy
Work done by lift chain
4. Compare the values you calculated in #3. Explain the significance of
this comparison.
This ride is for APC and APB only.
I
Instructions for APC
Locate one of the many fish that expel water from its mouth in a parabolic
path.
Take measurements that are necessary to calculate the velocity of water as
it exits the mouth of the fish. Provide the following:
•
•
•
Detailed sketch of the path showing important physics variables measured
Calculation scheme
% difference with at least one other group
Instructions for APB
Use the data taken from APC students.
1) The radius of the fountain’s exit hole is 4.0 x 10-3 m. Calculate the
volume flow rate of the water.
2) The fountain is fed by a pipe that has an opening of 7.0 x 10-3 m and is
below the fish at ground level. Calculate the gauge pressure in the
feeder pipe at this point.
The Forbidden Journey
The activity is for students who have Aaron
Shkoler as a calculus teacher.
Once per hour over the course of several hours take 5 minutes and count the number of patrons
who enter an Harry Potter:TFJ and the number of patrons who exit. Multiplying by 12 will give
the rate at which patrons enter/exit the attraction in people per hour. Let f ′ ( t ) be the rate at
which patrons enter the attraction in people per hour and g ′ ( t ) be the rate at which patrons exit
the attraction in people per hour over the measured interval.
Time
(hours)
1
2
3
4
5
6
f ′ (t )
g′ (t )
a) Use a trapezoidal approximation to estimate the number of people who have entered the
attraction during the 1st three hours.
b) Use a trapezoidal approximation to estimate the number of people inside the attraction
at the end of the 3rd hour.
c) During the third hour is the number of people inside the attraction increasing or
decreasing?
d) Approximate the hour during which the greatest number of people are inside the
attraction.