Source localization in ocean acoustics is posed as a machine learning problem in which data-driven methods learn source ranges d
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Answer:
a) ΔV₁ = 21.9 V, b) U₀ = 99.2 10⁻¹² J, c) U_f = 249.9 10⁻¹² J, d) W = 150 10⁻¹² J
Explanation:
Let's find the capacitance of the capacitor
C =
C = 8.85 10⁻¹² (8.00 10⁻⁴) /2.70 10⁻³
C = 2.62 10⁻¹² F
for the initial data let's look for the accumulated charge on the plates
C =
Q₀ = C ΔV
Q₀ = 2.62 10⁻¹² 8.70
Q₀ = 22.8 10⁻¹² C
a) we look for the capacity for the new distance
C₁ = 8.85 10⁻¹² (8.00 10⁻⁴) /6⁴.80 10⁻³
C₁ = 1.04 10⁻¹² F
C₁ = Q₀ / ΔV₁
ΔV₁ = Q₀ / C₁
ΔV₁ = 22.8 10⁻¹² /1.04 10⁻¹²
ΔV₁ = 21.9 V
b) initial stored energy
U₀ =
U₀ = (22.8 10⁻¹²)²/(2 2.62 10⁻¹²)
U₀ = 99.2 10⁻¹² J
c) final stored energy
U_f = (22.8 10⁻¹²) ² /(2 1.04 10⁻⁻¹²)
U_f = 249.9 10⁻¹² J
d) the work of separating the plates
as energy is conserved work must be equal to energy change
W = U_f - U₀
W = (249.2 - 99.2) 10⁻¹²
W = 150 10⁻¹² J
note that as the energy increases the work must be supplied to the system
Answer:
Approximately (assuming that air resistance is negligible.)
Explanation:
Let denote the initial velocity of this ball. Let
denote the angle of elevation of that velocity.
The initial velocity of this ball could be decomposed into two parts:
- Initial vertical velocity:
.
- Initial horizontal velocity:
.
If air resistance on this ball is negligible, alone would be sufficient for finding the time of flight of this ball.
Calculate given that
and
:
.
Assume that air resistance on this ball is zero. Right before the ball hits the ground, the vertical velocity of this ball would be exactly the opposite of the value when the ball was launched.
Since , the vertical velocity of this ball right before landing would be
.
Calculate the change to the vertical velocity of this ball:
.
In other words, the vertical velocity of this ball should have change by during the entire flight (from the launch to the landing.)
The question states that the gravitational field strength on this ball is . In other words, the (vertical) downward gravitational pull on this ball could change the vertical velocity of the ball by
each second. What fraction of a second would it take to change the vertical velocity of this ball by
?
.
In other words, it would take to change the velocity of this ball from the initial velocity at launch to the final velocity at landing. Therefore, the time of the flight of this ball would be
.