Mechanics> PHYSICS EXPERT Circular motion question...

A fighter plane is pulling out for a dive at 900 km/hr in a vertical circle of radius 2 km. Its mass is 5000 kg. ind the force exerted by the air on it at the lowest point.....and PLS EXPLAIN HOW???

Aditi Bhatnagar , 14 Years ago

Grade 12th Pass

1 Answers

Askiitians Tutor Team

To determine the force exerted by the air on the fighter plane at the lowest point of its dive, we need to consider the forces acting on the plane at that moment. The key forces include the gravitational force acting downward and the lift force generated by the air acting upward. Let's break this down step by step.

Understanding the Forces at Play

At the lowest point of the dive, the fighter plane experiences two main forces:

Weight (W)
Lift (L): This is the upward force generated by the air as the plane moves through it. At the lowest point, this lift must not only counteract the weight of the plane but also provide the necessary centripetal force to keep the plane moving in a circular path.

Calculating the Weight of the Plane

The weight of the plane can be calculated using the formula:

W = m × g

Where:

m = mass of the plane = 5000 kg

g = acceleration due to gravity = 9.81 m/s²

Substituting the values:

W = 5000 kg × 9.81 m/s² = 49050 N

Finding the Centripetal Force

Next, we need to calculate the centripetal force required to keep the plane moving in a circular path. The formula for centripetal force (Fc) is:

Fc = (m × v²) / r

Where:

v = velocity of the plane in meters per second (m/s)

r = radius of the circular path in meters (m)

First, we need to convert the speed from kilometers per hour to meters per second:

v = 900 km/hr × (1000 m/km) / (3600 s/hr) = 250 m/s

Now, substituting the values into the centripetal force formula:

Fc = (5000 kg × (250 m/s)²) / 2000 m

Fc = (5000 kg × 62500 m²/s²) / 2000 m = 156250000 N / 2000 = 78125 N

Calculating the Total Lift Force

At the lowest point, the total lift force must counteract both the weight of the plane and provide the necessary centripetal force. Therefore, we can express the lift force as:

L = W + Fc

Substituting the values we calculated:

L = 49050 N + 78125 N = 127175 N

Final Result

The force exerted by the air on the fighter plane at the lowest point of its dive is approximately 127175 N. This force is crucial for maintaining the plane's circular motion while ensuring it remains airborne against the force of gravity.