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Marat540 [252]
2 years ago
15

A large ant is standing on the middle of a circus tightrope that is stretched with tension Ts. The rope has mass per unit length

μ. Wanting to shake the ant off the rope, a tightrope walker moves her foot up and down near the end of the tightrope, generating a sinusoidal transverse wave of wavelength λ and amplitude A. Assume that the magnitude of the acceleration due to gravity is g.What is the minimum wave amplitude Amin such that the ant will become momentarily "weightless" at some point as the wave passes underneath it? Assume that the mass of the ant is too small to have any effect on the wave propagation.Express the minimum wave amplitude in terms of Ts, μ, λ, and g.
Physics
1 answer:
natta225 [31]2 years ago
8 0

Answer:

A = g (λ / 2π)² μ / Ts

Explanation:

The ant becomes "weightless" when its acceleration is equal to gravity.  The motion of the ant is a sinusoidal wave:

y = A sin(ωt)

By taking the derivative twice, we can find the acceleration of the ant:

y' = Aω cos(ωt)

y" = -Aω² sin(ωt)

The maximum acceleration occurs when sine is 1.  We want this to happen at a = -g.

-g = -Aω² (1)

A = g / ω²

Angular frequency is 2π times the normal frequency:

ω = 2πf

A = g / (2πf)²

Frequency is velocity divided by wavelength:

f = v / λ

A = g / (2πv / λ)²

A = g (λ / 2π)² / v²

Velocity of a wave in a string with tension Ts and linear density μ is:

v = √(Ts / μ)

Therefore:

v² = Ts / μ

Plugging in:

A = g (λ / 2π)² / (Ts / μ)

A = g (λ / 2π)² μ / Ts

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Answer:

2 x 10⁻³ volts

Explanation:

B = magnetic of magnetic field parallel to the axis of loop = 1 T

\frac{dA}{dt} = rate of change of area of the loop = 20 cm²/s = 20 x 10⁻⁴ m²

θ = Angle of the magnetic field with the area vector = 0

E = emf induced in the loop

Induced emf is given as

E = B \frac{dA}{dt}

E = (1) (20 x 10⁻⁴ )

E = 2 x 10⁻³ volts

E = 2 mV

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2 years ago
An automobile traveling at 25.0 km/h along a straight, level road accelerates to 65.0 km/h in 6.00 s. what is the magnitude of t
USPshnik [31]
Note that
1 km/h = (1000 m)/(3600 s) = 0.27778 m/s

Initial velocity, v₁ = 25 km/h = 6.9444 m/s
Final velocity, v₂ = 65 km/h = 18.0556 m/s

Time interval, dt = 6 s.

Calculate average acceleration.
a = (v₂ - v₁)/dt
   = (18.0556 - 6.9444 m/s)/(6 s)
   = 1.852 m/s²

Answer:
The average acceleration is 1.85 m/s² (nearest hundredth)
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2 years ago
The planets how and block are near each other in the Dorgon system. the Dorgons have very advanced technology, and a Dorgon scie
BlackZzzverrR [31]

Answer:

Decreasing the distance between Hox and Blox, increasing the mass of Hox, or increasing the mass of Hox and Blox.

Explanation:

The gravity force is directly proportional to the mass of the bodies and inversely proportional to the square of the distance that separates them.

Or

If we decrease the distance between both planets (Hox and Blox), the gravitational pull between them will increase.  

On the other hand, if we keep the distance between Hox and Blox, but we increase the mass of one of them, or increase the mass of both, the gravitational pull between them will also increase.

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An engineer uses aluminum to build an airplane rather than composite materials that are lighter and stronger. He does this becau
AleksandrR [38]

Answer:

choosing a material that will show warning before it fails

Explanation:

According to my research on different architectural engineering techniques, I can say that based on the information provided within the question this is an example of choosing a material that will show warning before it fails. By choosing aluminum he can detect certain failures a long time before it actually happens since aluminum shows signs of wear and tear and doesn't just break immediately.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

4 0
2 years ago
Read 2 more answers
A monkey weighs 6.00 x 102 N and swings from vine to vine. As the monkey grabs a new vine, both vines make an angle of 35.0° wit
zmey [24]

Answer:

T=366.23\ N

Explanation:

Given:

  • mass of monkey, w=600\ N
  • angle of vine from the vertical, \theta=35^{\circ}

Now follow the schematic to understand the symmetry and solution via Lami's theorem.

<u>The weight of the monkey will be balanced equally by the tension in both the vines:</u>

Using Lami's Theorem:

\frac{w}{sin\ 70^{\circ}} =\frac{T}{sin\ 145^{\circ}}

\frac{600}{sin\ 70^{\circ}} =\frac{T}{sin\ 145^{\circ} }

T=366.23\ N

4 0
2 years ago
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