In class, we built a model of a roller coaster that would be one-hundredth of the size of the roller coaster if it were to be built in real life. On the model we built, 3.38G's were recorded. Would the amount of G-forces on the model roller coaster remain the same on the roller coaster if it were to be built in real life?
If it was to be built in real life the difference in height will increase potential energy, the mass will increase, and therefore because it was increased uniformly F=MA acceleration will be constant.
so yes.
The forces will certainly not be the same but much smaller on the model. The acceleration is the question.
h = H/10^2
m = M/10^6 because volume is 1/100^3
V = sqrt (2 g H)
v = sqrt (2 g h)
so
v = V/10
acceleration is velocity /time
time is distance/velocity
so
acceleration = k * velocity^2/distance
a = k* 2 g h/h = 2 k g
A = k * 2 g H/H= 2 k g
so the accelerations are the same
Thank you
I also said that if the roller coaster was built in real life, it would have a faster velocity, since we were told to work out velocity by:
Change in potential energy + change in kinetic energy + (frictional force multiplied by distance)
Is this right?
yes
If you were a ship designer you would know that for a model and full scale under gravitation
v/sqrt(gL) is the same model and full scale.
if you divide the lengths by 100, you divide the speeds by 10
Google Froude number - here : http://www.engineeringtoolbox.com/froude-number-d_578.html
To determine whether the amount of G-forces on the model roller coaster would remain the same in real life, we need to understand what G-forces are and how they relate to the size of the roller coaster.
G-forces, or gravitational forces, refer to the acceleration experienced by an object due to the force of gravity. 1G is equivalent to the acceleration due to gravity on Earth, which is approximately 9.8 meters per second squared (m/s^2).
When building a model of a roller coaster, it's common to scale down the size while keeping the same proportions to fit the available space. In your case, you mentioned that the model is one-hundredth of the size of the real roller coaster. If we assume all other factors (such as curvature, speed, and incline) remain the same when scaling down, then the G-forces experienced on the model would also scale down proportionally.
To calculate the G-forces on the model roller coaster, we can multiply the acceleration due to gravity (1G or 9.8 m/s^2) by the acceleration factor, which is the reciprocal of the scale factor. In your case, the scale factor is 1/100, so the acceleration factor is 100.
G-forces on the model roller coaster = 9.8 m/s^2 * 100 = 980 m/s^2
Therefore, on the model roller coaster, 3.38G's would be equivalent to an acceleration of 3.38 * 9.8 m/s^2 = 33.164 m/s^2.
If we assume that the actual roller coaster is built with the same proportions and all other factors remain the same, the amount of G-forces on the real roller coaster would also scale proportionally. Thus, it would experience approximately 33.164 m/s^2 of acceleration, which is equivalent to 3.38G's.
In conclusion, the amount of G-forces on the model roller coaster would remain the same on the real roller coaster if all other factors and proportions are kept constant during the scaling process.