1.You are riding on a 20m diameter Ferris wheel. when your cart is at the bottom, you feel twice as heavy as you normally are. what is the speed of the wheel?
V^2/R = g
Solve for V
g is the acceleration of gravity.
Most Ferris wheels don't go that fast. If they did, you would feel weightless at the top. People would not like that - other amusement park rides can offer that experience.
To determine the speed of the Ferris wheel, we need to consider the gravitational force acting on you at the bottom of the ride and compare it to your usual weight.
At the bottom of the Ferris wheel, you experience an apparent weight twice as heavy as your normal weight. This increased apparent weight is due to the presence of an additional downward force called the centripetal force, which is necessary for circular motion.
To calculate the centripetal force, we can use the formula:
Fc = m * ac
Where:
Fc is the centripetal force,
m is your mass,
and ac is the centripetal acceleration.
Since we want to find the speed of the Ferris wheel, we can express the centripetal acceleration in terms of the velocity:
ac = v^2 / r
Where:
v is the velocity of the Ferris wheel,
and r is the radius of the Ferris wheel (half the diameter).
First, we need to find your normal weight (W_normal). Weight can be calculated using the formula:
W = m * g
Where:
m is your mass,
and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Since at the bottom of the Ferris wheel, your apparent weight is twice your normal weight, we can set up the equation:
2 * W_normal = Fc
Substituting the values, we have:
2 * m * g = m * ac
Now, we can substitute ac with v^2/r:
2 * m * g = m * (v^2 / r)
We can cancel out the mass (m) from both sides:
2 * g = v^2 / r
Finally, solving for v (velocity), we can rearrange the equation as follows:
v^2 = 2 * g * r
Taking the square root of both sides:
v = √(2 * g * r)
Now, let's plug in the values given in the question:
r = 20m (radius is half the diameter, which is 20m),
g = 9.8 m/s^2 (acceleration due to gravity).
Calculating the velocity, we have:
v = √(2 * 9.8 m/s^2 * 20m)
v ≈ √(392)
v ≈ 19.8 m/s
So, the speed of the Ferris wheel is approximately 19.8 meters per second.