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

The apparent weight that the pilot feels at the bottom of the loop-the-loop is calculated by summing the gravitational force and the centripetal force, resulting in an apparent weight of 4012.9 N.

Step-by-step explanation:

The student's question is asking to calculate the apparent weight that a pilot feels at the bottom of a loop-the-loop. To find the apparent weight, we must calculate the normal force on the pilot, which is the combination of the gravitational force and the centripetal force required to keep the pilot in a circular path at the bottom of the loop.

Firstly, we calculate the gravitational force (weight) acting on the pilot: W = m × g, where m is the mass of the pilot, and g is the acceleration due to gravity. For the pilot with a mass of 84.0 kg, W = 84.0 kg × 9.8 m/s² = 823.2 N.

Next, we determine the centripetal force required for circular motion at the bottom of the loop: Fc = (mv²) / R, where m is the mass, v is the constant speed, and R is the radius of the loop. With v = 345 m/s and R = 3.033 km (or 3033 m), Fc = (84.0 kg × (345 m/s)²) / 3033 m = 3189.7 N.

The apparent weight of the pilot at the bottom of the loop is the sum of the gravitational force and the centripetal force: Apparent weight = W + Fc = 823.2 N + 3189.7 N = 4012.9 N.

Therefore, the pilot feels an apparent weight of 4012.9 N at the bottom of the loop-the-loop.

Answer 2

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

Step-by-step 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+(mv^2)/(R)`

⇒
`N=mg(1+(v^2)/(Rg) )`

⇒
`N=mg(1+((345)^2)/(3.033* 10^3 * 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.