How many revolutions per minute would a 16m -diameter Ferris wheel need to make for the passengers to feel "weightless" at the topmost point?
All I want to know is where do I start?
I thought I would set a(centripital accelteration) = (9.8 m/s^2)?
Oops nevermind realized I was using 2(pi)r^2 and not 2(pi)r.
So set a(c) = 9.8, and use a= v^2/r so find v. Then, use the equation for velocity.
your calculated v will be in m/s
the question asks for rpm
60 s in a min and circumference = 2πr
(60 v) / (2 π r)
To determine the number of revolutions per minute required for the passengers on the Ferris wheel to feel "weightless" at the topmost point, you can start by using the centripetal acceleration formula.
1. Start by identifying the given information:
- Diameter of the Ferris wheel (d) = 16m
- Acceleration due to gravity (g) = 9.8 m/s^2
2. Next, calculate the radius of the Ferris wheel (r) using the formula:
r = d/2 = 16m / 2 = 8m
3. The passengers will feel "weightless" at the topmost point when the net force acting on them is equal to zero. In this case, the net force will be the difference between the gravitational force and the centripetal force.
4. The gravitational force (Fg) acting on the passengers can be calculated using the following formula:
Fg = m * g
Where "m" is the mass of the passengers (which is not given).
5. The centripetal force (Fc) acting on the passengers can be determined by the formula:
Fc = m * ac
Where "ac" is the centripetal acceleration.
6. Since the passengers feel "weightless" at the topmost point, the net force (Fn) is equal to zero:
Fn = Fc - Fg = 0
7. Based on the above equation, we can set up the following relationship:
m * ac - m * g = 0
8. Rearrange the equation to solve for the centripetal acceleration (ac):
ac = g
9. Now that we have determined the centripetal acceleration, we can use it to find the velocity (v) of the Ferris wheel at the topmost point. Since the Ferris wheel completes a full circle every revolution, the velocity can be calculated as:
v = 2 * pi * r / t
Where "t" is the time taken to complete one revolution.
10. At the topmost point, the velocity is at its minimum, which means the centripetal acceleration equals the gravitational acceleration. So, we can set up the following equation:
ac = v^2 / r
11. Substitute the value of the centripetal acceleration (g) into the equation above:
g = v^2 / r
12. Rearrange the equation to solve for the velocity (v) at the topmost point:
v = sqrt(g * r)
13. Finally, to find the number of revolutions per minute, divide the velocity by the circumference of the Ferris wheel and then convert to minutes:
Number of revolutions per minute = v / (2 * pi * r) * 60
So, by following these steps, you can determine the number of revolutions per minute required for the passengers to feel "weightless" at the topmost point of the Ferris wheel.