A fighter jet is traveling at 200 m/s following the arc of a vertical circle of radius R. At the top of its path, the pilot experiences “weightlessness.” What is the value of R?
4,000 meters
To find the value of R, we need to analyze the forces acting on the fighter jet at the top of its path when the pilot experiences weightlessness.
At the top of the path, two forces are acting on the jet: the gravitational force (mg) pulling it downwards, and the centripetal force (mv^2/R) pulling it towards the center of the circle. The centripetal force is responsible for keeping the jet in circular motion.
In this case, the gravitational force must be equal to the centripetal force for the pilot to experience weightlessness. So, we have:
mg = mv^2/R
Simplifying this equation, we cancel out the mass (m) from both sides:
g = v^2/R
Now, we can substitute the given values into this equation. You mentioned that the fighter jet is traveling at 200 m/s. So, we can plug this value into the equation:
9.8 m/s^2 = (200 m/s)^2 / R
Next, we can simplify further by squaring the velocity:
9.8 m/s^2 = 40,000 m^2/s^2 / R
To solve for R, we rearrange the equation:
R = 40,000 m^2/s^2 / 9.8 m/s^2
Evaluating this expression, we find:
R ≈ 4081.63 meters (or approximately 4082 meters)
Therefore, the value of R is approximately 4082 meters.