The planar simple harmonic wave travels in the positive direction of x axis with wave velocity u=2m/s, and the vibration curve o
f the particle at the origin in cosinusoidal form is shown in the figure.
Try to find (1) the vibration function of the particle at the origin, (2) the wave function of the planar simple harmonic wave according to the origin.
Try to find (1) the vibration function of the particle at the origin, (2) the wave function of the planar simple harmonic wave according to the origin.
2 answers:
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Answer:
a) 0.28 m or 28 cm is the minimum height above ground the fish reaches.
b) at the height of 0.484 m height , the pufferfish will eventually come to rest.
c) There exists two types of energy remain at the equilibrium point in the system. These are :
Gravitational potential energy = 23.72J
Spring potential energy = 0.384 J
Explanation:
Given that :
Mass of the pufferfish m =5kg
initial height of the fish h =5.5m
length of the spring l =0.5m
Spring constant K =3000N/m
a)
Assuming no energy loss to friction, what is the minimum height above the ground that the pufferfish reaches?
Lets assume that the minimum height the fish reaches is = x meters
Now by using the conservation of energy; we realize that :
Initial total energy = final total energy
Gravitational potential energy =
Gravitational potential energy' + Spring potential energy (kinetic energy is zero in both cases)
Replacing our given values into the above equation; we have :
269.5 = 47.5 x + 1500(0.5 -x )²
269.5 = 47.5 x + 1500(0.25 - x²)
269.5 = 47.5 x + 375 - 1500 x²
269.5 - 375 = 47.5 x - 1500 x²
-105.5 = 47.5 x - 1500 x²
-105.5 + 1500 x² - 47.5 x = 0
1500 x² - 47.5 x - 105.5 = 0
By using quadratic equation and taking the positive value;
x = 0.28 m or 28 cm is the minimum height above ground the fish reaches.
b)
At the equilibrium position the weight of fish will be equal to the force applied by the spring thus
mg = kx
substituting our given values ; we have:
(5)(9.8) = 3000x
x = 61.22
x = 0.016m : so this is the compression in the spring
Now; to determine the height the pufferfish gets to before it eventually come to rest; we have
(0.5-0.016) m = 0.484m
therefore, at the height of 0.484 m height , the pufferfish will eventually come to rest.
c)
There exists two types of energy remain at the equilibrium point in the system. These are :
Gravitational potential energy = mgh' = (5)(9.8)(0.484)
= 23.72J
and spring potential energy
Answer:
F = -319.2 N
Explanation:
Given that,
The mass of a bicyclist, m = 70 kg
Mass of the bicycle = 9.8 kg
The speed of a bicycle, v = 16 m/s
We need to find the magnitude of the braking force of the bicycle come to rest in 4.0 m.
The braking force is given by :
So, the required force is 319.2 N.