At an amusement park there is a ride in which cylindrically shaped chambers spin around a central axis. People sit in seats facing the axis, their backs against the outer wall. At one instant the outer wall moves at a speed of 3.2 m/s, and an 83 kg person feels a 525 N force pressing against his back. What is the radius of the chamber?
To find the radius of the chamber, we can use the following equation:
Force = Mass x Acceleration
In this case, the force pressing against the person's back is the centripetal force, given by:
Centripetal Force = Mass x (Velocity^2 / Radius)
Given that the mass of the person is 83 kg, the velocity is 3.2 m/s, and the centripetal force is 525 N, we can rearrange the equation to solve for the radius:
Radius = (Mass x Velocity^2) / Centripetal Force
Plugging in the values:
Radius = (83 kg x (3.2 m/s)^2) / 525 N
Simplifying:
Radius = (83 kg x 10.24 m^2/s^2) / 525 N
Radius = (848.32 kg*m^2/s^2) / 525 N
Radius ≈ 1.617 m
Therefore, the radius of the cylindrical chamber is approximately 1.617 meters.
To find the radius of the chamber, we can use the concept of centripetal force. Centripetal force is the force acting on an object moving in a circular path, directed toward the center of the circle.
The formula to calculate centripetal force is given by:
F = (m * v^2) / r
Where:
F = centripetal force
m = mass of the object
v = velocity of the object
r = radius of the circular path
In this case, we are given the mass of the person (83 kg), the velocity of the outer wall (3.2 m/s), and the force pressing against the person's back (525 N).
Rearranging the formula, we can solve for the radius (r):
r = (m * v^2) / F
Plugging in the values, we get:
r = (83 kg * (3.2 m/s)^2) / (525 N)
Calculating this expression will give us the radius of the chamber.
Fc = mv^2/r
Fc is given and v is given. Substitute and solve for r