A 1500kg car traveling along a road is hit by a 0.1kgrock that creates a small crack in the car’s windshield. Which of the follo
2 answers:
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If gravitational effects from other objects are negligible, the speed of the rock at a very great distance from the planet will approach a value of
<u>Explanation:</u>
To express velocity which is too far from the planet and escape velocity by using the energy conservation, we get
Rock’s initial velocity
, . Here the radius is R, so find the escape velocity as follows,
Where, M = Planet’s mass and G = constant.
From given conditions,
Surface potential energy can be expressed as,
R tend to infinity when far away from the planet, so
Then, kinetic energy at initial would be,
Similarly, kinetic energy at final would be,
Here,
Now, adding potential and kinetic energies of initial and final and equating as below, find the final velocity as
'm' and as common on both sides, so gets cancelled, we get as
We know, , it can be wriiten as
, we get
Taking squares out, we get,
Answer:
w = √ 1 / CL
This does not violate energy conservation because the voltage of the power source is equal to the voltage drop in the resistence
Explanation:
This problem refers to electrical circuits, the circuits where this phenomenon occurs are series RLC circuits, where the resistor, the capacitor and the inductance are placed in series.
In these circuits the impedance is
X = √ (R² + ( -
)² )
where Xc and XL is the capacitive and inductive impedance, respectively
X_{C} = 1 / wC
X_{L} = wL
From this expression we can see that for the resonance frequency
X_{C} = X_{L}
the impedance of the circuit is minimal, therefore the current and voltage are maximum and an increase in signal intensity is observed.
This does not violate energy conservation because the voltage of the power source is equal to the voltage drop in the resistence
V = IR
Since the contribution of the two other components is canceled, this occurs for
X_{C} = X_{L}
1 / wC = w L
w = √ 1 / CL