Question

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?

Answer 1

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.

Answer 2

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

Answer 3

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?

Answer 4

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