Answer: 0.0146m
Explanation: The formula that defines the velocity of a simple harmonic motion is given as
v = ω√A² - x²
Where v = linear velocity, A = amplitude = 1.69cm = 0.0169m, x = displacement.
The maximum speed of a simple harmonic motion is derived when x = A, hence v = ωA
One half of maximum speed = speed of motion
3ωA/2 = ω√A² - x²
ω cancels out on both sides of the equation, hence we have that
A/2 = √A² - x²
(0.0169)/2 = √(0.0169² - x²)
0.00845 = √(0.0169² - x²)
By squaring both sides, we have that
0.00845² = 0.0169² - x²
x² = 0.0169² - 0.00845²
x² = 0.0002142
x = √0.0002142
x = 0.0146m
Answer:
The speed of the two cars after coupling is 0.46 m/s.
Explanation:
It is given that,
Mass of car 1, m₁ = 15,000 kg
Mass of car 2, m₂ = 50,000 kg
Speed of car 1, u₁ = 2 m/s
Initial speed of car 2, u₂ = 0
Let V is the speed of the two cars after coupling. It is the case of inelastic collision. Applying the conservation of momentum as :
V = 0.46 m/s
So, the speed of the two cars after coupling is 0.46 m/s. Hence, this is the required solution.
Answer:
A) 11.28 x 10^(7) A.m²
B) 2.258 x 10^(17)A
Explanation:
A) The current density is given by the formula ;
J = nqv
Where n is the density of protons in the solar wind which is 12.5 cm³ or 12.5 x 10^(-6) m³
q is the proton charge which is 1.6 x 10^(-19) C
v is velocity which is 564km or 564000m
Thus, J = 12.5 x 10^(-6) x 1.6 x 10^(-19) x 564000 = 11.28 x 10^(7) A.m²
B) the formula for the total current the earth received is given as;
I = JA
The effective area is the cross section of the earth and thus,
Area = πr² where r is the radius of the earth given as: 6.371 x 10^(6)
A = π(6.371 x 10^(6)) ²
So I = 11.28 x 10^(7) x π(6.371 x 10^(6))² = 2.258 x 10^(17)A
