Question

Самолет делает «мертвую петлю» радиусом 500 м с постоянной скоростью 360 км/ч. Найти вес летчика в верхней точке петли, если масса летчика равна 70 кг

Answer 1

Вес лётчика в верхней точке = mU^2/R - mg = m(U^2/r - g) = 714 Н.

Answer 2

Calculation of the Pilot's Weight at the Top of the Loop

To find the weight of the pilot at the top of the loop, we can use the centripetal force equation:

F = m * a

where: - F is the centripetal force, - m is the mass of the pilot, and - a is the acceleration.

In this case, the centripetal force is provided by the gravitational force acting on the pilot:

F = m * g

where g is the acceleration due to gravity.

At the top of the loop, the centripetal force is equal to the gravitational force:

m * g = m * a

Since the pilot is in uniform circular motion, the acceleration can be expressed as:

a = v^2 / R

where: - v is the velocity of the plane, and - R is the radius of the loop.

Given that the radius of the loop is 500 m and the velocity of the plane is 360 km/h (or 100 m/s), we can substitute these values into the equation:

m * g = m * (v^2 / R)

Simplifying the equation, we can solve for the mass of the pilot:

m = (g * R) / v^2

Now we can calculate the weight of the pilot at the top of the loop using the given mass of 70 kg.

Calculation:

Using the equation m = (g * R) / v^2, we can substitute the values:

m = (9.8 m/s^2 * 500 m) / (100 m/s)^2

Calculating this expression, we find:

m ≈ 49 kg

Therefore, the weight of the pilot at the top of the loop is approximately 49 kg.