Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle with a radius of 600 m. At the bottom of the dive, the speed of the airplane is 150 m/s. What is the apparent weight
Of the 70-kg pilot at that point?
A) 1400 N
B) 490 N
C) 690 N
D) 2600 N
E) 3300 N

Question

Quizplus · Accepted Answer

The apparent weight of the pilot can be calculated using the formula for centripetal force, which is necessary to keep the pilot moving in a circle, plus the force of gravity. The centripetal force (Fc) is given by $ F_c = \frac{mv^2}{r} $, where $m$ is the mass, $v$ is the velocity, and $r$ is the radius of the circle. The force of gravity (Fg) acting on the pilot is $ F_g = mg $, where $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$). The apparent weight is the sum of these two forces.Given:- $m = 70 \, kg$- $v = 150 \, m/s$- $r = 600 \, m$- $g = 9.8 \, m/s^2$First, calculate the centripetal force:$$ F_c = \frac{70 \times (150)^2}{600} = \frac{70 \times 22500}{600} = \frac{1575000}{600} = 2625 \, N $$Then, calculate the force of gravity:$$ F_g = 70 \times 9.8 = 686 \, N $$The apparent weight is the sum of $ F_c $ and $ F_g $:$$ F_{apparent} = F_c + F_g = 2625 + 686 = 3311 \, N $$Rounding to the nearest hundred gives us approximately 3300 N, which corresponds to choice E.

Pulling Out of a Dive, the Pilot of an Airplane