Silly Serpent Answers
Background
This is a ride which is designed to create a mild thrill. This is caused not by the speed at
which the rider moves but the acceleration which the rider experiences. In the human body
there are accelerometers inside the skull in the region of the ears (semicircular canals). These
tubes detect an increase or decrease in speed or a change in direction. The thrill in the ride
comes from the rapid change in direction. This is experienced either with the eyes open or
shut and does not rely upon visual information from the retina. The acceleration is related to
the velocity squared and inversely to the radius. So – go faster or turn sharper. The force the
body experiences is dependant on the acceleration.
The ride involves a series of energy transformations. Electrical energy is transformed by the
motor into kinetic and gravitational potential energy.
Drawings
1)
2)
Draw the shape of the track
a)
Label the points on the
track where you would
experience;
b)
The highest speed
c)
The highest acceleration
d)
The highest gravitational
potential energy
e)
The highest kinetic energy
c
d on top
b& e
Draw a diagram of you sitting in a carriage at the highest point on the track
during the ride. Draw in all the forces acting on you at this point. . Label the
forces as “Force by A on You”.
Weight down (F by Earth on You) &
Normal reaction up (F by Seat on You) &
forward push from the seat (F by seat on You)
3.
On the drawing of the first two cars below draw in the forces acting on the
Serpent car as the ride starts off.
Normal reaction (F by track on wheels)
Carriage
Backward Tension force
from Carriage
(F by Carriage on Serpent)
4.
Serpent
Driving Force
(Force by Track on Wheels)
Weight
(F by Earth on Serpent)
Using another coloured (red) pen draw in the net force acting on a passenger
in the carriage at this point.
Estimations
Your mass 70 kg. The mass of the empty carriage 700 kg
Height of rail at the lowest point 0.50 m. Maximum height of the rail 4.0 m
Number of curves 2x180 and 1x 360 The radius of each curve 2x5m and 1x3m.
Distance traveled by the Serpent in one second about 3.0 m.
The total circumference of each curve added to give the total distance around the
track ½ (2  5)x2 + 2x3 + three straight lengths 5m + 6m + 8m= 69m m.
Measure the time for one rotation of the serpent = 15seconds.
Stopping distance = 4.0 m. Stopping time = 2.0 s.
Calculations (include units)
1)
Using your estimation for the total distance around the track calculate your
average velocity as you complete one circuit.
V= d/t = 69/15 = 4.6 m/s
2)
Using the average velocity and the radius for each curve, calculate the
centripetal acceleration on you.
a= v2/r = 4.6x4.6/5 = 4.m/s/s and the 360 curve a = v2/r = 4.6 x 4.6 /3= 7m/s/s
3)
Using the formula for gravitational potential energy, work out your change in
potential energy as the serpent ride lifts you from the lowest point to the
highest point.
PE = mgh = 70 x 9.8 x (4- 0.5)= 2.4x103 Joules
What is your total energy at this point in the ride?
Energy = PE + KE = 2.4 x103 + 1/2mv2 = 2.4 x103 + ½70x4.62 = 3.1 x103 J
4)
Count the maximum possible number of passengers and the number of
carriages . Calculate the maximum total mass of passengers when the ride is
full. Use this with the average velocity to calculate the maximum momentum
of the Serpent ride.
20 people with an average mass of say 50kg (more little kids than adults normally
momentum = mass x velocity = 20 x 50 x 4.6 = 4.6 x103 kg m/s. this is the
momentum for the passengers. There are 5 carriages with a mass of 2x 500kg
and 3 x 300kg Carriage momentum = Mv = 1900 x 4.6 = 8.7 x103
Total momentum 8.7 x103+ 4.6 x103 = 1.3 x104 kgm/s
5)
When the ride stops what happens to this momentum? transferred to the Earth
6)
Calculate the braking force required to stop the whole ride.
change in momentum is 1.3 x104 = Impulse
= Force x time = Force = impulse /time = 1.3 x104 /2seconds = 6.7 x103 Newtons
7)
Work out the total kinetic energy of the serpent ride before it stops.
KE = ½ mv2
8)
= 0.5x2900 x4.6x 4.6 =
3.1 x104 Joules
What happens to this energy when the Serpent stops?
Kinetic energy changed into heat & sound
Unit 3 Detailed Study: Materials and their use in structures
1)
Draw one of the arms of the vertical
support structure for the rail.
2)
Indicate which parts of the structure are in
tension none & all are in compression.
3)
Which part of the structure (if any) could
be replaced by cables? none
4)
Using your mass and the number of passengers in one carriage and looking
just at a single stationary carriage, use estimations of the fully loaded carriage
mass to work out the net downward force acting on the track.
weight = mg = (70 x 4 +300) x 9.81 = 5690 N
5)
______________________________________________________________
If this one carriage is over one structural leg- calculate the stress on this leg
using an estimation of the inner 2cm and outer 3cm radius of the leg.
thickness area of steel = R2 - r2 = ( 0.032 - 0.022 ) = 1.6x10 -3 m 2
stress = force/area = 5690 / 1.6x10 -3
= 3.6 x10 6 Nm-2
______________________________________________________________
6)
What material is the leg made from and why?
steel – strong, tough, ductile, cheap
Unit 4 Electric Power: Drive
1)
What powers the serpent? AC or DC? ….. Give evidence for your conclusion.
The power arriving into the Park is delivered from the street in cables protected by
“tiger tubing” to prevent high vehicles shorting out the power. The voltage will be
240 volts AC 50Hz (it could use 480 V AC but this is unlikely). It could be 3 phase
to deliver more power. The ride is electric – it has 2 thick copper power rails – a
live and a neutral – which is likely to be at earth voltage and connected to the
bodywork for safety. The motor is electric because electric motors can generate
much higher accelerations in short bursts than petrol engines. The motor/motors
is/are likely to deliver about 20KW of power (about 80 amps). Or they might be DC
voltage.. What do you think?
2)
Is the ride powered by one motor at the front or more? Two motors one at the
front & one under the last carriage
3)
Determine the starting force provided by the Serpent assuming the ride is to
start with an acceleration of 1m/s2 and using your total carriage mass
estimation.
Force = mass x acceleration = 2900 x 1 = 2900Newtons
4)
If the motor is low voltage (100V), what current would be drawn by the 10kW
motor as it moves the carriages?
Power = voltage x current
5)
a single motor current = 10000/100 = 100amps
Over the first 4 seconds what is the amount of energy drawn from the motor?
Energy = power x time = 10000 x 4 = 40000 Watts
6)
Use the amount of energy drawn from the motor over one second and the
estimation of the total mass of the Serpent ride with carriages and passengers
plus the distance traveled in that second. Calculate the theoretical
acceleration of the Serpent.
The ride is never going at constant speed. It is always getting faster/slower/turning.
In the first second the motors accelerate the train from u=0 and travels about 3m
Energy = 10,000Joules = Force x distance= Mxaxd = 2900x3xa a = 1m/s/s
7)
What are the safety issues which need to be considered when operating this
kind of ride? Electrical safety – keeping the passengers and the operator from
touching live wires, preventing mechanical failure which results in damaged track
or vehicles causing injury, structural soundness in the supports – with checks for
fatigue, mechanical wear and corrosion, especially at the joints, failsafe on the
electronic control to ensure there is an acceleration limiter
8)
What keeps the Serpent from toppling off the track?
The body & seating is low to the track (keeping the centre of mass low) & the
wheels are lower and curl around the track gripping it (although the track is quite
narrow) grip the side.
9)
What drives the Serpent – wheels, rollers, pulleys, cogs, chains or ropes?
A driven cog system under the body of the snake
10)
Where are the brakes on the Serpent?
On each of the carriage wheels