Question

A pilot, whose mass is 84.0 kg, makes a loop-the-loop in a fast jet. Assume that the jet maintains a constant speed of 345 m/s and that the radius of the loop-the-loop is 3.033 km. What is the apparent weight that the pilot feels (i.e., the force with which the pilot presses against the seat) at the bottom of the loop-the-loop?

Answer 1

Answer:

The apparent weight is 5 times greater than the original weight at the bottom.

Explanation:

Given:

Mass of the pilot, m = 84 kg

Velocity of the jet, v = 345 m/s

Radius of the loop, R = 3.033 km = 3.033 * 10^3 m

We have to find the apparent weight that the pilot feels.

Let the apparent weight be "N" .

Apparent weight :

• It is based on where is the position of the pilot in the loop-the-loop.
• The apparent weight is the highest at the bottom of the loop-the-loop.
• Because the weight acts down and the normal force acts towards the center of the circle.

From the FBD shown we can say that :

apparent weight (N)

⇒ $N=mg+\frac{mv^2}{R}$

⇒ $N=mg(1+\frac{v^2}{Rg} )$

⇒ $N=mg(1+\frac{(345)^2}{3.033\times 10^3 \times 9.8} )$

⇒ $N=5mg$

Therefore,

The force exerted by the seat on the pilot at the bottom of the loop is greater than the pilots weight by a factor of 5.