Roller Coaster Calculations
1.Calculate speed at the bottom of the hill.
Use 10 meters/second2 for the acceleration due to gravity (g).
Calculate the velocity at the bottom of the first hill. Assume the initial
velocity is zero. (“d” is the dropping distance from the top of the first hill!)
Record the distance in m. Use the following equation.
2gd
Velocity =
4. Calculate the Centripetal Acceleration of a flat Curve.
a. Calculate the velocity.
b. Measure the radius of the curve.
c. Use the formula to calculate acceleration.
𝑣2
𝑎=
𝑟
Practice Problems
1. Calculate the speed and G-forces at the bottom of each hill.
2. Calculate G-forces at the dip of a hill.
a. Calculate the radius of your dip (r). “d” is the distance from the top of the
first hill to the bottom of your curve:
2gd
25
r =
=
4
5
Height of Hill
(m)
𝑑
r
3. Calculate G-forces for your loop.
a. Calculate the radius for the top of your loop.
2gd
45
b. Calculate the G-forces at the top of the loop. You should not exceed 3.5
G-forces at the top of the loop.
Gs =
2d
1
r
c. Calculate the G-forces at the side of the loop.
Gs =
2d
r
Velocity (m/s)
G-force
10
50
b. Calculate the G-forces at this dip. Make sure that you do not exceed 4.0
G-forces.
2d
Gs =
1
r =
Radius (m)
100
2. Calculate the G-forces of the loops.
Height of
Loop (m)
Radius (m)
G-force at the
top of the loop
G-force on the
side of the loop
50
30
10
3. A car is rounding a curve at a speed of 25 m/s. If the radius of the curve
is 30 m, what was the car’s centripetal acceleration?