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 3.78 m/s, and an 63.5-kg person feels a 528-N force pressing against his back. What is the radius of a chamber?
To determine the radius of the chamber, we can use the concept of centripetal force, which is the force that keeps an object moving in a circular path.
The force pressing against the person's back is the result of the centripetal force acting on them due to their circular motion. This force can be calculated using the equation:
F = (m * v^2) / r
Where:
F is the centripetal force (528 N),
m is the mass of the person (63.5 kg),
v is the speed of the outer wall (3.78 m/s),
and r is the radius of the chamber (unknown).
Rearranging the equation, we can solve for the radius (r):
r = (m * v^2) / F
Substituting the given values:
r = (63.5 kg * (3.78 m/s)^2) / 528 N
Calculating this, we get:
r = (63.5 kg * 14.2884 m^2/s^2) / 528 N
r = 905.5946 kg·m²/s² / 528 N
r ≈ 1.7163 meters
Therefore, the radius of the chamber is approximately 1.7163 meters.