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 (the force that the pilot exerts on the seat)of the 70-kg pilot at that point?
A)3300 N
B)690 N
C)2600 N
D)490 N
E)1400 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:$$F_c = \frac{mv^2}{r} = \frac{70 \times 150^2}{600} = \frac{70 \times 22500}{600} = \frac{1575000}{600} = 2625 \, N$$Then, calculate the force of gravity:$$F_g = mg = 70 \times 9.8 = 686 \, N$$The apparent weight is the sum of $F_c$ and $F_g$:$$2625 \, N + 686 \, N = 3311 \, N$$Rounding to the nearest hundred gives approximately $3300 \, N$, which matches choice A.

Pulling Out of a Dive,the Pilot of an Airplane Guides