Question

В низшей точке "мёртвой петли" вес лётчика составляет 7,2 кН. масса лётчика 80 кг, радиус петли 320 м. Определить скорость самолёта. Ускорение свободного падения принять равным 10 м/с^2

Answer 1

P=m*g+mV^2/R
m*V^2/R=P-m*g
V=sqrt(P-m*g)*R/m)=sqrt(7200-80*10)*320/80)=160 м

Answer 2

Calculation of the Airplane's Speed in a Loop-the-Loop

To determine the speed of the airplane in a loop-the-loop, we can use the principle of centripetal force. In a loop-the-loop, the centripetal force is provided by the weight of the pilot. The formula for centripetal force is:

F = m * a

Where: - F is the centripetal force - m is the mass of the pilot - a is the centripetal acceleration

In this case, the centripetal force is equal to the weight of the pilot, which is given as 7.2 kN (kilonewtons). The mass of the pilot is 80 kg, and the radius of the loop-the-loop is 320 m. The acceleration due to gravity can be taken as 10 m/s^2.

Using the formula for centripetal force, we can solve for the acceleration:

F = m * a

7.2 kN = 80 kg * a

Converting the centripetal force to Newtons:

7.2 kN = 7200 N

Solving for the acceleration:

7200 N = 80 kg * a

a = 7200 N / 80 kg

a = 90 m/s^2

Now that we have the centripetal acceleration, we can calculate the speed of the airplane using the formula for centripetal acceleration:

a = v^2 / R

Where: - v is the speed of the airplane - R is the radius of the loop-the-loop

Rearranging the formula, we get:

v = sqrt(a * R)

Substituting the values:

v = sqrt(90 m/s^2 * 320 m)

v = sqrt(28800 m^2/s^2)

v ≈ 169.71 m/s

Therefore, the speed of the airplane in the loop-the-loop is approximately 169.71 m/s.