Newton's Laws of Motion on a helicopter

In summary, the task is to calculate the force exerted by the air on the blades of a helicopter as it lifts a truck with an upward acceleration of 0.9 m/s2. The solution depends on whether the helicopter is hovering or accelerating with the truck. In the case of hovering, the weight of the helicopter and truck must be calculated and added to the additional acceleration of 0.9 m/s2. If the helicopter is also accelerating, then its inertial acceleration must also be added to the calculation. The acceleration of gravity is assumed to be 9.81 m/s2.
  • #1
brriney
3
0

Homework Statement



A 12000- kg helicopter is lifting a 4000- kg truck with an upward acceleration of 0.9 m/s2. Calculate the force the air exerts on the helicopter blades.

Homework Equations



F = ma

The Attempt at a Solution



I have no idea! Please help!
 
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  • #2
Well the answer depends on whether the helicopter is hovering (stationary) or is also accelerating with the truck.

Let's assume the helicopter is hovering. It has a weight which is the product of its mass and the acceleration of gravity.

Now looking at the truck, it also has a weight which is the product of its mass and the acceleration due to gravity, but the helicopter is pulling it up with an additional acceleration of 0.9 m/s2, so one has to add that acceleration to the acceleration of gravity to get the combined force.


If the helicopter is also accelerating then one has to add that inertial acceleration to the acceleration of gravity.

g = 9.81 m/s2
 
  • #3


I understand your confusion and am happy to provide guidance. In this scenario, we can use Newton's Second Law of Motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). We can also use Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction.

In this case, the force the air exerts on the helicopter blades is equal to the force the helicopter exerts on the air, but in the opposite direction. This means that we can calculate the force on the blades by first determining the force exerted by the helicopter on the air, and then using Newton's Third Law to find the force on the blades.

To find the force exerted by the helicopter on the air, we can use the equation F = ma, where m is the mass of the helicopter and a is the upward acceleration of 0.9 m/s2. This gives us a force of 10,800 N (F = 12,000 kg x 0.9 m/s2).

Now, using Newton's Third Law, we know that the force on the blades is equal to the force on the air, but in the opposite direction. Therefore, the force on the blades is also 10,800 N, but in the downward direction.

I hope this helps to clarify the situation and provide a solution to the problem. Keep in mind that Newton's Laws of Motion are fundamental principles that explain the behavior of objects in motion, and can be applied to a wide range of scenarios.
 

1. What are Newton's Laws of Motion?

Newton's Laws of Motion are a set of three physical laws that describe the behavior of objects in motion. They were formulated by Sir Isaac Newton in the 17th century and are considered fundamental principles in the study of mechanics.

2. How do Newton's Laws apply to a helicopter?

Newton's Laws apply to a helicopter in the same way they apply to any other object in motion. The first law, also known as the Law of Inertia, states that an object will remain at rest or in uniform motion unless acted upon by an external force. In a helicopter, this means that the helicopter will remain still or continue to fly in a straight line unless the pilot applies force to change its motion.

3. How does the second law of motion affect a helicopter?

The second law of motion, also known as the Law of Acceleration, states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. In a helicopter, this means that the amount of force the rotor blades exert on the air determines the acceleration of the helicopter. A larger force will result in a greater acceleration, while a larger mass will result in a smaller acceleration.

4. Can you explain how Newton's third law applies to a helicopter?

The third law of motion, also known as the Law of Action and Reaction, states that for every action, there is an equal and opposite reaction. In a helicopter, this means that the downward force exerted by the rotor blades on the air creates an equal and opposite upward force, allowing the helicopter to lift off the ground and stay in the air. This is also known as Bernoulli's principle.

5. How do Newton's Laws affect the stability of a helicopter?

Newton's Laws play a crucial role in the stability of a helicopter. The first law ensures that the helicopter will maintain its state of motion unless acted upon by an external force, allowing it to remain stable in flight. The second law dictates how much lift and thrust the helicopter needs to stay in the air, while the third law ensures that the forces acting on the helicopter are balanced, preventing it from tipping over. Overall, Newton's Laws help keep the helicopter stable and in control during flight.

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