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 3.44 m/s, and an 64.3-kg person feels a 277-N force pressing against his back. What is the radius of a chamber?
To find the radius of the chamber, we can use the concept of centripetal force. In this scenario, the force pressing against the person's back is the centripetal force acting towards the center of rotation.
The formula for centripetal force is:
F = m * (v^2 / r)
Where:
F is the centripetal force,
m is the mass of the person,
v is the velocity of the outer wall, and
r is the radius of the chamber.
We are given:
F = 277 N,
m = 64.3 kg,
v = 3.44 m/s.
Rearranging the formula, we have:
r = (m * (v^2)) / F
Substituting the given values:
r = (64.3 kg * (3.44 m/s)^2) / 277 N
Evaluating this expression, we can find the radius of the chamber.