The ride I am going to study is called 'Detonator', it uses both the physics principles I explained above, below is a picture
Physics Coursework-
Physics principles that can be observed in a Theme Park
Introduction
Physics is a large subject that can be observed almost everywhere, even in a theme park, in a theme park physics principles such as 'weightlessness' and 'acceleration/deceleration' play a large part in ensuring that the rides are as thrilling as they are safe. In this essay I am going to show how two certain physics principles are being used in a ride to ensure that the ride is safe but at the same time delivers a lot of thrill to the rider. I am going to explore the sense of 'weightlessness' during freefall, and how 'forces' are used to ensure that the ride is not dangerous, I will also mention how gravitational potential energy converts to kinetic energy as the ride drops.
Physics principles
Weightlessness
Freefall is a term used to describe how an object is moving through the air when there are practically no forces other than gravity acting on them. During freefall, object experience a sense of 'weightlessness', but weightlessness does not mean that an object loses all its weight. Since in Physics 'weight' does not mean how heavy an object is, (that is known as the 'mass') 'weight' is a term used to describe how much force and object is exerting due to gravity, weight can only be felt if there is another force opposing the direction of the weight, as stated by Newton's laws of motion that 'all forces have a resistant force that is equal to and in the opposite direction of the force', on earth the resistant force is delivered by the ground beneath our feet, so if the ground was taken away, as in freefall, there would be no resistant force and we would not experience weight, that is what is meant by the term 'weightlessness'. This is used in the ride I am going to study to create the feeling to falling into a pit and thus creating a thrill.
Stopping forces
Another physics principle I am going to explore is the use of forces to ensure that the ride is safe, specifically stopping forces. A stopping force is, as suggested by the name, is the force needed to stop an object from moving in a certain direction. This stopping force results in a deceleration of the object, the stopping force (F) is calculated by multiplying the 'mass' (m) by the acceleration (a), so they are linked by the formula,
Force =mass x acceleration.
Acceleration is a term used to describe how much faster an object is getting, usually per second, it is calculated by taking the change in velocity (speed in a given direction, usually in m/s) (initial velocity 'u', minus the finishing velocity 'v'), and dividing it by the time taken for this change 't' usually in seconds, this can be written as
Acceleration = Change in velocity
Time taken for change
or
a=v-u
t
The units for acceleration are ms-2 or m/s². The 'mass' ...
This is a preview of the whole essay
Force =mass x acceleration.
Acceleration is a term used to describe how much faster an object is getting, usually per second, it is calculated by taking the change in velocity (speed in a given direction, usually in m/s) (initial velocity 'u', minus the finishing velocity 'v'), and dividing it by the time taken for this change 't' usually in seconds, this can be written as
Acceleration = Change in velocity
Time taken for change
or
a=v-u
t
The units for acceleration are ms-2 or m/s². The 'mass' is, as stated above, how heavy an object is, usually in kilograms (kg). The force itself is measured in Newtons (N) after sir Isaac Newton. In the ride I am going to study, stopping forces are taken into consideration in deciding how powerful to make the brakes in order to stop the ride in time.
Gravitational potential to kinetic energy
Energy cannot be destroyed or created, it can only be transferred to another type of energy, in the case of the ride I am going to study, gravitational potential energy (energy an object has stored due to gravity) is converted to kinetic energy (energy an object has whilst it's moving). In order to work these out we use the formulas below
Gravitational potential energy=mass x acceleration due to gravity x change in height
Kinetic energy = 1/2 x mass x velocity²
If we exclude the force of friction then if we minus the two values, we can wok out how much energy is lost as heat.
Location
For this coursework, I visited a theme park called 'Thorpe Park', an amusement park full of thrilling rides that use physics to create the maximum thrill whilst still keeping the ride safe and keeping the passengers out of harms way. The ride I am going to study is called 'Detonator', it uses both the physics principles I explained above, below is a picture of the ride, it involves pulling a platform of 14 seats up to a certain height, before dropping the platform into freefall towards the ground and stopping the ride just in time.
Estimation
Method
As you can see from the diagram below, the measurements are estimated using a method of similar triangles, below it is how it works.
The ruler is levelled up with the height of the ground, the object is then moved along the ruler till it reaches the level of the building, the measurement of the height of the object is taken as well as the distance of the measuring point to the structure and the length along the ruler, we can then use similar triangles where X/h1=h/d, thus the height of the actual structure would be X/h1, x d. Below are the measurements I took at the ride:
Height of object 15cm, 0.15m
Length along ruler, for height of ride 33cm, 0.33m for height of brakes 14cm, .14m
Distance from structure 1630cm, 16.3m
So the height of the ride would be X=0.33m
h1=0.15m
d=16.3m
h=0.33/0.15=2.2
x16.3
h=35.86m
And the height of the brake would be X =0.14m
h1=0.15m
d=16.3m
h=0.14/0.15=0.93
x16.3
h=15.44m
Time in freefall 2s
Time braking 0.7s
Since these are estimates they are not totally reliable, therefore there may be some inaccuracies and limits in how accurate my conclusions are.
The ride
Below is a simplified diagram of the ride, in order to analyse and show where the physics principles come into action, I am going to split the ride into two parts, when its in freefall and when its braking.
Calculations
Velocity during freefall
Whilst the ride is in freefall, it is accelerating due to gravity, which is approximately 9.81ms-2 , the ride took approximately 2s to drop from the top of the ride down to where it starts braking, which is a distance of approximately 20.42m, from this I can work out how fast the ride is travelling on average, using the formula of
Velocity²= initial velocity² x 2 x acceleration x distance travelled
V²=u² + 2as
If we substitute the values in:
U=0
A=9.81ms-2
S=20.42m
V²=0² + 2 x 9.81 x 20.42
V²=400.6404
V=V400.6404
V=20.02ms-1
So the ride is travelling at a speed of 20.02ms-1 by the end of the freefall.
Stopping force
After it has been in freefall which is where most of the thrill occurs, the ride begins to brake using a magnetic brake, I can work out the force this magnet exerts on the ride in order to stop, it using the formula I mentioned above,
force=mass x acceleration,
as I mentioned earlier, the ride has a platform of 14 seats, if we consider the average adult at 90kg, when full, the platform could weigh 90x14=1260kg, this is a very rough estimate as I have not included the masses of the seats themselves and the mass of the platform itself, which could limit the accuracy of my results. The acceleration would be worked out using the equation above,
acceleration= change in velocity u
the time taken for the change.
The initial velocity would be 20.02ms-1 (above), the end velocity would 0 since the ride has stopped, the time taken for the change is the 0.7s. If we once again substitute the number in, the change in velocity would be 20.02-1, so we would do 20.02/0.7 to work out acceleration, which comes 28.6ms-2 .
Now that we have the acceleration, we can work out the stopping force, if we use the mass as the highest value, then the stopping force of the brake would be 28.6x1260= 36036N, which is a large stopping force needed to stop the high speed that the ride drops you at.
Gravitational Potential energy
From the values we have, we can also work out the transfer of Gravitational potential energy (stored energy an object has due to gravity) to kinetic energy (energy an object has when moving). Below is a diagram that shows how the gravitational potential energy and the kinetic energy change as the ride drops.
To work out the gravitational potential energy we use the formula mentioned above:
Gravitational potential energy = mass x acceleration due to gravity x change in height.
Gpe=mgh
This stored energy is then converted to kinetic energy as the platform drops, in order to work out the kinetic energy, we use the formula:
Kinetic energy = 1/2mass x velocity².
k.e.=1/2mv²
If we exclude friction and air resistance, then
Gpe=k.e.
So
Mgh=1/2mv²
And if we divide both sides by 'm', then
gh=1/2v²
if we then work out the gravitational potential energy at the top of the ride:
g=9.81ms-2
h=35.86m
gpe=9.81 x 35.86
=351.787J
if we also work out the kinetic energy just before it brakes
v=20.02ms-1
k.e.=1/2 x 20.02²
=1/2 x 400.800
=200.400J
If we subtract them, we will be able to work out how much energy is lost as heat:
351.787-200.400
=151.387J lost as heat energy
Problems and Limitations
Throughout the coursework I may have made errors and inaccuracies, these can limit how accurate my results and conclusions are. I have identified some of the in the essay itself, but I will highlight them now. The largest inaccuracy and problem in the work I have done is that I used more or less only estimations and mostly trusted my own judgement when estimating, which can lead to severe inaccuracies in my work, but I believe my estimation are largely correct or near the actual number.
Another large error is that I have not included value or made certain values negligible, as I mentioned above I did not include the mass of the seats and the platform when I estimated the mass to avoid unnecessary errors in my work, another I have not included in my calculations is the force of friction which could have lowered the overall speed of the ride since not all the gravitational potential energy (stored energy an object has due to gravity) would have been converted to kinetic energy (movement energy an object has), which are other physics principles I could have analysed and looked at when studying the ride.
Future developments
The same physics principles could be used to make a larger or different version of the ride. An idea would be that people are placed in seats in a transparent plastic capsules, which is then dropped down a tube onto a cushion type material to cushion the blow, below is a diagram of how it would look, the material would have to be carefully chosen in order to make sure it is soft enough and compresses enough to absorb the entire impact, in order to make the ride twice as fast, the ride would have to be more than eight times as high because if we re-arrange the equation for kinetic energy and gravitational potential, then
/2mv²=mgh
We can cancel the m's
/2V²=gh
If we multiply by 2
V²=2gh
And then square root
V=V2gh
In order to double the velocity, we must multiply be two on both sides
2V = 2V2gh
= V4x2gh
Which makes
2V=V8gh
So the height has to be 8 times larger in order to double the velocity
And the cushion would have to have a even larger stopping force to make sure the person is stopped in time, but it would have to dent in a lot in order to avoid causing any damage to the passenger or the capsule.
