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Q. 60

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 157

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Short Answer

Starting from rest, a helicopter accelerates straight up at a constant What is the helicopter's height at the moment its blades are providing an upward force of ? The helicopter can be modeled as a -m-diameter sphere.

The height of which a helicopter lifted by providing an upward force is

See the step by step solution

Step by Step Solution

Step 1: Given

The mass of a helicopter is and the acceleration of the helicopter straight up is . The upward force exerted by the helicopter is. The diameter of the sphere is .

The weight of the helicopter act downward and the motion of the helicopter is in vertically upward. So, the drag force exerted by the air on the helicopter act vertically downward.

Step 2: Formula used.

To calculate the lifting velocity of the helicopter using Newton's law is,

  • is the mass of the helicopter.
  • is the drag force.
  • is the constant acceleration.
  • is the acceleration due to gravity.

Formula to calculate the drag force on the helicopter by assuming it as a sphere is,

  • is the diameter of the sphere.
  • is the velocity of the helicopter uplifted.
  • is the density of air.

Step 3: Calculation.

Substitute for in equation (I).

The density of air is generally

Substitute for for for for and for to find .

.

Step 4: Calculation.

Formula to calculate the vertical distance of the helicopter is,

  • is the initial velocity of the helicopter.
  • is the vertical height of the helicopter lifted.

Substitute for for and for to find .

Step 5: Conclusion.

Therefore, the height of which a helicopter lifted by providing an upward force is

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