the condition of apparent weightlessness for the passengers can be created for a brief instant when a plane flies over the top of a vertical circle. at a speed of 215 meters per second, what is the radius of the vertical circle that the pilot must use?
but what is m?
you wont need m, the m, in both sides of the equation cancel each other
To find the radius of the vertical circle that the pilot must use, we need to use the concept of centripetal force.
In this scenario, the apparent weightlessness experienced by the passengers is due to the fact that the normal force exerted by the seat on the passengers is equal to zero. This occurs when the gravitational force and the centripetal force are in balance.
The gravitational force (Fg) acting on the passengers is given by the equation:
Fg = m * g
Where m is the mass of the passenger and g is the acceleration due to gravity (approximately 9.8 m/s^2).
The centripetal force (Fc) required to maintain circular motion is given by the equation:
Fc = (m * v^2) / r
Where v is the velocity of the plane and r is the radius of the vertical circle.
In the condition of apparent weightlessness, the normal force is zero, which means the gravitational force (Fg) is equal to the centripetal force (Fc):
Fg = Fc
m * g = (m * v^2) / r
We can rearrange this equation to solve for r:
r = (m * v^2) / (m * g)
Let's plug in the given values:
v = 215 m/s
g = 9.8 m/s^2
As the mass (m) cancels out, we can calculate the radius:
r = (215^2) / 9.8
r = 4642.14 meters
Therefore, the pilot must use a radius of approximately 4642.14 meters in order to create the condition of apparent weightlessness for the passengers flying at a speed of 215 meters per second.