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Chapter 6: Problem 57

While hovering, a typical flying insect applies an average force equal to twice its weight during each downward stroke. Take the mass of the insect to be \(10 \mathrm{~g}\), and assume the wings move an average downward distance of \(1.0 \mathrm{~cm}\) during each stroke. Assuming 100 downward strokes per second, estimate the average power output of the insect.

Short Answer

Expert verified
The average power output of the insect is \(0.196W\).

Step by step solution

01

Determine the Weight of the Insect

Weight is the force exerted by a body due to gravity. It is determined using the equation \(Weight = mass \times gravity\). Given that the mass of the insect is \(10g = 0.01kg\) and the acceleration due to gravity is \(9.8 m/s^2\), the weight of the insect can be calculated as \(Weight = 0.01 \times 9.8 = 0.098N\).
02

Determine the Force Applied

The insect applies a force twice its weight during each stroke. Therefore, the force applied can be determined by doubling the weight. Thus, \(Force = 2 \times Weight = 2 \times 0.098 = 0.196N\).
03

Determine the Work Done Per Stroke

Work done can be determined using the equation \(Work = Force \times Distance\). The given distance per stroke is \(1.0cm = 0.01m\). Thus, the work done per stroke is \(Work = Force \times Distance = 0.196 \times 0.01 = 0.00196J\).
04

Determine the Power Output

Power is the amount of work done per unit time. It can be determined using the equation \(Power = Work / Time\). With 100 strokes per second, the time per stroke is \(1/100s\). Thus, the power can be calculated as \(Power = Work / Time = 0.00196 / (1/100) = 0.196W\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Force in Hovering Insects
When we talk about force in the context of insects, we're referring to the push or pull that an insect exerts while flying. Specifically, for a hovering insect, this force comes into play when the insect flaps its wings. The downward stroke is particularly crucial as it propels the insect upward, countering the force of gravity.
  • The force exerted by the insect is directly related to its weight.
  • A typical hovering insect applies a force equal to twice its weight during the downward stroke.
  • This is necessary to maintain a stable hovering position, allowing the insect to balance gravity effectively.
In physics, this force is measured in newtons (N). Calculating it involves knowing the insect's weight, which is the product of its mass and the acceleration due to gravity.
Exploring Work Done by Insect Wings
Work can be thought of as the effort applied over a distance. In the case of insect flight, work is done every time the insect's wings move. When wings push down on the air, they are performing work to lift the insect up.
  • Each stroke corresponds to a specific amount of work done by the insect.
  • Work done is computed using the formula: \(Work = Force \times Distance\).
  • For our insect, the wing moves down by \(1\,cm\), equating to \(0.01\,m\).
This equation helps us calculate the energy expended in moving the wings downwards. Essentially, the insect converts its energy into mechanical work, enabling flight.
What Makes a Hovering Insect?
Hovering insects are fascinating because they're able to suspend themselves mid-air without moving forward or backward. This ability is crucial for various tasks, such as feeding or adjusting their position in the environment.
  • To hover, an insect must regularly exert force to counteract gravity.
  • The insect performs rapid wing flaps, sometimes reaching over 100 times per second.
  • This constant movement keeps the insect aloft by balancing forces.
Hovering requires significant energy because maintaining a position in mid-air involves continuous work. As such, the metabolic demands on these creatures are high, leading them to efficiently manage their power output.
The Mechanics of Insect Flight
Insect flight is a marvel of nature, involving complex physical principles to enable sustained air travel. What sets insect flight apart is the unique wing motion which simultaneously generates lift and thrust.
  • To achieve flight, an insect must generate a lift greater than its body weight.
  • This is accomplished through rapid and repetitive wing beats.
  • Each wing beat produces a controlled amount of power to maintain altitude and direction.
Thus, the power output in insect flight is a reflection of the energy conversion from the insect's metabolic stores into the mechanical work of its wings. The power generated ensures that the insect can remain in flight, adjust its speed, and navigate its surroundings effectively.

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Most popular questions from this chapter

A force \(\vec{F}\) that is at an angle \(60^{\circ}\) above the horizontal is applied to a box that moves on a horizontal frictionless surface, and the force does work \(W\) as the box moves a distance \(d\). (a) At what angle above the horizontal would the force have to be directed in order for twice the work to be done for the same displacement of the box? (b) If the angle is kept at \(60^{\circ}\) and the box is initially at rest, by what factor would \(F\) have to be increased to double the final speed of the box after moving distance \(d ?\)

A \(75.0 \mathrm{~kg}\) painter climbs a ladder that is \(2.75 \mathrm{~m}\) long and leans against a vertical wall. The ladder makes a \(30.0^{\circ}\) angle with the wall. (a) How much work does gravity do on the painter? (b) Does the answer to part (a) depend on whether the painter climbs at constant speed or accelerates up the ladder?

A small glider is placed against a compressed spring at the bottom of an air track that slopes upward at an angle of \(40.0^{\circ}\) above the horizontal. The glider has mass \(0.0900 \mathrm{~kg}\). The spring has \(k=640 \mathrm{~N} / \mathrm{m}\) and negligible mass. When the spring is released, the glider travels a maximum distance of \(1.80 \mathrm{~m}\) along the air track before sliding back down. Before reaching this maximum distance, the glider loses contact with the spring. (a) What distance was the spring originally compressed? (b) When the glider has traveled along the air track \(0.80 \mathrm{~m}\) from its initial position against the compressed spring, is it still in contact with the spring? What is the kinetic energy of the glider at this point?

You are applying a constant horizontal force \(\vec{F}=\) \((-8.00 \mathrm{~N}) \hat{\imath}+(3.00 \mathrm{~N}) \hat{\jmath}\) to a crate that is sliding on a factory floor. At the instant that the velocity of the crate is \(\overrightarrow{\boldsymbol{v}}=(3.20 \mathrm{~m} / \mathrm{s}) \hat{\imath}+\) \((2.20 \mathrm{~m} / \mathrm{s}) \hat{\jmath},\) what is the instantaneous power supplied by this force?

A \(5.00 \mathrm{~kg}\) block is moving at \(v_{0}=6.00 \mathrm{~m} / \mathrm{s}\) along a frictionless, horizontal surface toward a spring with force constant \(k=500 \mathrm{~N} / \mathrm{m}\) that is attached to a wall (Fig. P6.79). The spring has negligible mass. (a) Find the maximum distance the spring will be compressed. (b) If the spring is to compress by no more than \(0.150 \mathrm{~m},\) what should be the maximum value of \(v_{n} ?\)
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