A revolving searchlight on an island 6 miles from shore turns at the rate of 2 revolutions per minute in the clockwise direction
1 answer:
Answer:
Revolving velocity = 2 km/s
Explanation:
Velocity of circular motion = Radius x Angular velocity.
Angular velocity, ω = 2πf, where f is the frequency of circular motion.
Here frequency, f = 2 revolutions per minute
f = revolutions per second.
Angular velocity, ω = 2πf = 0.209 radians/second.
Radius = 6 miles = 6 x 1.6 x 10³ = 9.6 x 10³ m.
Linear velocity = 9.6 x 10³ x 0.209 = 2006.4 m/s= 2 km/s
Revolving velocity = 2 km/s
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Answer:
The gravitational force between m₁ and m₂, is approximately 1.06789 × 10⁻⁶ N
Explanation:
The details of the given masses having gravitational attractive force between them are;
m₁ = 20 kg, r₁ = 10 cm = 0.1 m, m₂ = 50 kg, and r₂ = 15 cm = 0.15 m
The gravitational force between m₁ and m₂ is given by Newton's Law of gravitation as follows;
Where;
F = The gravitational force between m₁ and m₂
G = The universal gravitational constant = 6.67430 × 10⁻¹¹ N·m²/kg²
r₂ = 0.1 m + 0.15 m = 0.25 m
Therefore, we have;
The gravitational force between m₁ and m₂, F ≈ 1.06789 × 10⁻⁶ N
The spring has been stretched 0.701 m
Explanation:
The elastic potential energy of a spring is the potential energy stored in the spring due to its compression/stretching. It is calculated as
where
k is the spring constant
x is the elongation of the spring with respect to its equilibrium position
For the spring in this problem, we have:
E = 84.08 J (potential energy)
k = 342.25 N/m (spring constant)
Therefore, its elongation is:
Learn more about potential energy:
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