A Device for Training Astronauts and Jet Fighter Pilots
What is the speed at which the trainee is revolving in the device?
The trainee in the device is revolving at a speed of approximately 9.81 m/s or 0.15 rev/s.
Calculating Trainee's Speed
Radius of the circle (r) = 11.0 m
Force felt by the trainee = 7.45 times her own weight
In this scenario, the force felt by the trainee is given as 7.45 times her own weight. The force experienced by an object moving in a circle is the centripetal force, which is provided by the tension in the device. In this case, the centripetal force is equal to the gravitational force acting on the trainee.
Let's denote the trainee's weight as W. The centripetal force is then 7.45W. The centripetal force can also be expressed as the product of the trainee's mass (m) and the acceleration towards the center of the circle (a), which is given by the formula a = v^2 / r, where v is the speed and r is the radius of the circle.
Equating the centripetal force equations, we have 7.45W = m * (v^2 / r). Since W = mg, where g is the acceleration due to gravity, we can substitute and simplify the equation to 7.45mg = m * (v^2 / r). The mass cancels out, giving 7.45g = v^2 / r.
Solving for v, we find v = √(7.45g * r). Substituting the values of g = 9.81 m/s^2 and r = 11.0 m, we get v = √(7.45 * 9.81 * 11.0) ≈ 9.81 m/s. This is the speed at which the trainee is revolving.
To express the answer in rev/s, we divide the speed by the circumference of the circle. The circumference of a circle is 2πr, so the trainee's speed in rev/s is approximately 9.81 m/s / (2π * 11.0 m) ≈ 0.15 rev/s.