A particle of mass m moves under an attractive central force F(r) = -Kr4 with angular momentum L. For what energy will the motio
n be circular, and what is the radius of the circle? Find the frequency of radial oscillations in the particle is given a small radial impulse.
1 answer:
Answer:
Angular velocity is same as frequency of oscillation in this case.
ω = x
Explanation:
- write the equation F(r) = -K with angular momentum <em>L</em>
- Get the necessary centripetal acceleration with radius r₀ and make r₀ the subject.
- Write the energy of the orbit in relative to r = 0, and solve for "E".
- Find the second derivative of effective potential to calculate the frequency of small radial oscillations. This is the effective spring constant.
- Solve for effective potential
- ω = x
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Answer:
(a). The draw-down at a distance 200 m from the well after pumping for 50 hr is 5.383 m.
(b). The draw-down at a distance 200 m from the well after pumping for 50 hr is 6.707 m.
Explanation:
Given that,
Energy
Transmissivity
Storage coefficient
Distance r= 200 m
We need to calculate the draw-down at a distance 200 m from the well after pumping for 50 hr
Using formula of draw-down
Put the value into the formula
We need to calculate the draw-down at a distance 200 m from the well after pumping for 200 hr
Using formula of draw-down
Put the value into the formula
Hence, (a). The draw-down at a distance 200 m from the well after pumping for 50 hr is 5.383 m.
(b). The draw-down at a distance 200 m from the well after pumping for 200 hr is 6.707 m.