Question7. (II) (a) What magnitude force is required to give a helicopter of mass $M$ an acceleration of 0.10 g upward? (b) What work is done by this force as the helicopter moves a distance $h$ upward?

Studdy Solution

STEP 1

1. The helicopter has a mass $M$ .
2. The acceleration of the helicopter is $0.10g$ upward, where $g$ is the acceleration due to gravity.
3. We need to find the magnitude of the force required for this acceleration.
4. We need to calculate the work done by this force as the helicopter moves a distance $h$ upward.

STEP 2

1. Calculate the force required for the given acceleration.
2. Calculate the work done by this force over a distance $h$ .

STEP 3

Calculate the force required for the given acceleration.
To find the force, we use Newton's second law of motion, $F = ma$ .
The total acceleration $a$ is the sum of the gravitational acceleration $g$ and the additional acceleration $0.10g$ .
Thus, the total acceleration is: $a = g + 0.10g = 1.10g$
The force required is: $F = M \cdot a = M \cdot 1.10g$

STEP 4

Calculate the work done by this force over a distance $h$ .
The work done $W$ by a constant force is given by the formula: $W = F \cdot d \cdot \cos(\theta)$
Since the force is acting in the same direction as the displacement (upward), the angle $\theta = 0^\circ$ , and $\cos(0^\circ) = 1$ .
Thus, the work done is: $W = F \cdot h = (M \cdot 1.10g) \cdot h$
The magnitude of the force required is $M \cdot 1.10g$ , and the work done by this force as the helicopter moves a distance $h$ upward is $(M \cdot 1.10g) \cdot h$ .

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