Question

We can model the motion of a bumblebee's wing as simple harmonic motion. A bee beats its wings 250 times per second, and the wing tip moves at a maximum speed of 2.5 m/s . Part A What is the amplitude of the wing tip's motion?

Answer 1

Answer:

The amplitude of the wing tip's motion is 1.6 mm.

Explanation:

Given that,

Beat = 250 /s

Speed = 2.5 m/s

We need to calculate the amplitude of the wing tip's motion

Using the equation for the maximum velocity

$v_{max}=2\pi f A$

$A=\dfrac{v}{2\pi f}$

Where,

v = speed

f = frequency

A = amplitude

Put the value into the formula

$A=\dfrac{2.5}{2\pi\times250}$

$A=0.00159 = 1.59\times10^{-3}\ m$

$A=1.6\ mm$

Hence, The amplitude of the wing tip's motion is 1.6 mm.

Answer 2

The amplitude of the wing tip's motion is about 1.6 mm

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Further explanation

Simple Harmonic Motion is a motion where the magnitude of acceleration is directly proportional to the magnitude of the displacement but in the opposite direction.

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The pulled and then released spring is one of the examples of Simple Harmonic Motion. We can use the following formula to find the period of this spring.

$T = 2 \pi\sqrt{\frac{m}{k}}$

T = Periode of Spring ( second )

m = Load Mass ( kg )

k = Spring Constant ( N / m )

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The pendulum which moves back and forth is also an example of Simple Harmonic Motion. We can use the following formula to find the period of this pendulum.

$T = 2 \pi\sqrt{\frac{L}{g}}$

T = Periode of Pendulum ( second )

L = Length of Pendulum ( kg )

g = Gravitational Acceleration ( m/s² )

Let us now tackle the problem !

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Given:

frequency of the wings = f = 250 Hz

maximum speed of the wings = v_max = 2.5 m/s

Asked:

amplitude of the wing tip's motion = A = ?

Solution:

$v = \omega \sqrt{A^2 - x^2}$

$v_{max} = \omega \sqrt{A^2 - 0^2}$

$v_{max} = \omega A$

$v_{max} = 2 \pi f A$

$2.5 = 2 \pi \times 250 \times A$

$2.5 = 500 \pi \times A$

$A = 2.5 \div (500 \pi)$

$A \approx 1.6 \times 10^{-3} \texttt{ m}$

$A \approx 1.6 \texttt{ mm}$

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Learn more

• Model for Simple Harmonic Motion : brainly.com/question/9221526
• Force of Simple Harmonic Motion : brainly.com/question/3323600
• Example of Simple Harmonic Motion : brainly.com/question/11892568

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Answer details

Grade: High School

Subject: Physics

Chapter: Simple Harmonic Motion