Reference no: EM13964963
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 A 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.
Hint 1. Weight and weightless: Weight is generally defined as the force due to the gravitational attraction of a mass toward the earth. Weightless is a more colloquial term meaning that if you stepped on a scale (e.g., in a falling elevator) it would read zero.
Hint 2. How to approach the problem: In the context of this problem, when will the ant become weightless?
-When it has no net force acting on it
-When the normal force of the string equals its weight
-When the normal force of the string equals twice its weight
-When the string has a downward acceleration of magnitude g
Hint 3. Putting it all together
Once you have an expression for the maximum acceleration of a point on the string A max, determine what amplitude is required such that A max = -g . This will be the minimum amplitude A min for which the ant becomes weightless.
I have posted the other hint in this attachment but the answer for the previous hint was actually the last choice
Hint 2. How to approach the problem:
In the context of this problem, when will the ant become weightless?
When the string has a downward acceleration of magnitude
Correct
The ant will become weightless when the normal force between the string and the ant becomes zero. Once this happens, gravity is the only force acting on the ant; the ant will become weightless and will accelerate downward under the influence of gravity alone.
This same effect can be observed, to a lesser degree, in an elevator. When an elevator accelerates downward, we feel lighter. If this downward acceleration is equal to then we feel effectively weightless.
To solve this problem, you must determine the amplitude for which the maximum acceleration of a point on the string is equal to -g .
Hint 3. Find the maximum acceleration of the string
Assume that the wave propagates as y(x,t) = Asin(ωt- kx). What is the maximum downward acceleration amax of a point on the string?
Express the maximum downward acceleration in terms of Π and any quantities given in the problem introduction.
Hint 4. Putting it all together
Once you have an expression for the maximum acceleration of a point on the string amax , determine what amplitude is required such that amax= -g. This will be the minimum amplitude amin for which the ant becomes weightless.
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