A 1/10th scale model of an airplane is tested in a wind tunnel. The reynolds number of the model is the same as that of the full

The well-known equation... E = m c²... does not address the origin of the mass involved.

Converting 1 kg of any mass entirely into energy generates

(1kg) · (c²) Joules of energy.

E = (1 kg) · (c²) = (1 kg) · (299,792,458 m/s)²

E = 8.9876 x 10¹⁶ Joules

To simplify, this equates to the energy needed to keep a 100-watt light bulb illuminated for about 10,402,259,010 days.

(This is roughly 28.5 million years, based on the current understanding of days and years.)

Explanation:

Data provided:

Area A = 10 cm×2 cm = 20×10⁻⁴ m²

Separation distance d between the plates = 1 mm = 1×10⁻³ m

Battery voltage, or emf = 100 V

Resistance = 1025 ohm

Solution:

In an RC circuit, the voltage across the plates varies with time t. At the outset, the voltage matches that of the battery, V₀ = emf = 100V. However, after a certain time t, both the resistance and capacitance alter this, leading to a final voltage V expressed as

Applying the natural logarithm to both sides,

       (1)

Next, we can determine the capacitance using the plates' area.

C = ε₀A/d

  =

  = 18×10⁻¹²F

We can now find the time it takes for the voltage to drop from 100 to 55 V by substituting C, V₀, V, and R values into equation (1)

 = -(1025Ω)(18×10⁻¹² F) ln( 1 - 55/100)

 = 15×10⁻⁹s

= 15 ns

The gravitational force between Royce and Earth would double by the age of 16. Newton’s law of universal gravitation states that the gravitational force is proportional to the masses involved and inversely proportional to the square of the distance between them. At age 10, Royce weighed 30 kg, and by age 16, he weighed 60 kg. Since his mass doubled from 10 to 16 years, this results in a corresponding doubling of the gravitational force.