A raindrop has a mass of 8.7 × 10-7 kg and is falling near the surface of the earth. Calculate the magnitude of the gravitational force exerted (a) on the raindrop by the earth and (b) on the earth by the raindrop.
Well we all know that action is equal in magnitude and opposite in direction to reaction.
|F| = m g = 8.7 * 10^-7 * 9.81 = 8.53*10^-6 Newtons
Let's first establish the specifications: the mass of the raindrop is 8.7 × 10⁻⁷ kg.
(a) To calculate the magnitude of the gravitational force exerted on the raindrop by the Earth, we can use the formula:
F = G * (m₁ * m₂) / r²
Where:
F = gravitational force
G = gravitational constant
m₁ = mass of the raindrop
m₂ = mass of the Earth
r = distance between the center of the raindrop and the center of the Earth
As we're considering that both m₁ (mass of the raindrop) and r (distance between them) are very small compared to the Earth, we can simplify the equation:
F = G * (m₁ * m₂) / r² ≈ G * m₁ * m₂ / r²
The gravitational constant G is approximately equal to 6.674 × 10⁻¹¹ N * (m/kg)², and the mass of the Earth m₂ is approximately 5.972 × 10²⁴ kg. Since the distance (r) between the raindrop and the Earth's center was not given, we have to assume it's negligible here.
So, plugging in the values:
F = (6.674 × 10⁻¹¹ N * (m/kg)²) * (8.7 × 10⁻⁷ kg * 5.972 × 10²⁴ kg) / r²
However, since we're not given the distance between the raindrop and the Earth's center, we cannot accurately calculate the gravitational force in this case. Unfortunately, my funny calculations are thrown off by the lack of essential information. I apologize for the bummer!
(b) As I mentioned earlier, without the accurate distance, we won't be able to determine the force exerted on the Earth by the raindrop. Let's just say, it's enough to cause a tiny shiver in some earthworms.
Sorry for falling short on providing you with a proper answer. Feel free to ask me another question or share a joke to lighten the mood!
To calculate the magnitude of the gravitational force exerted on the raindrop by the Earth, you can use the formula:
F = m * g
Where:
F is the gravitational force
m is the mass of the raindrop
g is the acceleration due to gravity (approximately 9.8 m/s^2)
(a) On the raindrop by the Earth:
F = (8.7 × 10^-7 kg) * (9.8 m/s^2)
F ≈ 8.5 × 10^-6 N
The gravitational force exerted on the raindrop by the Earth is approximately 8.5 × 10^-6 Newtons.
(b) On the Earth by the raindrop:
According to Newton's third law of motion, the force exerted on the Earth by the raindrop is equal in magnitude but opposite in direction to the force exerted on the raindrop by the Earth. Hence, the magnitude of the gravitational force on the Earth by the raindrop is also approximately 8.5 × 10^-6 Newtons.
To calculate the magnitude of the gravitational force exerted on the raindrop by the earth and on the earth by the raindrop, we can use Newton's Law of Universal Gravitation.
The formula for calculating the gravitational force between two objects is:
F = (G * m1 * m2) / r^2
where,
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2 / kg^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
(a) To calculate the gravitational force exerted on the raindrop by the earth:
Given:
Mass of the raindrop, m1 = 8.7 × 10^-7 kg
Mass of the earth, m2 = Mass of the earth ≈ 5.972 × 10^24 kg (approximate value)
Distance between the raindrop and the center of the earth, r = Radius of the earth ≈ 6.371 × 10^6 m (approximate value)
Substituting the values into the formula:
F = (G * m1 * m2) / r^2
= (6.67430 × 10^-11 N m^2 / kg^2) * (8.7 × 10^-7 kg) * (5.972 × 10^24 kg) / (6.371 × 10^6 m)^2
Calculating this will give you the magnitude of the gravitational force exerted on the raindrop by the earth.
(b) To calculate the gravitational force exerted on the earth by the raindrop:
The gravitational force between two objects is mutual, which means that the force exerted on one object by another is equal in magnitude but opposite in direction to the force exerted on the second object by the first.
Since the gravitational force between the raindrop and the earth is the same, the magnitude of the force exerted on the earth by the raindrop will be the same as the magnitude of the force exerted on the raindrop by the earth.
Therefore, the magnitude of the gravitational force exerted on the earth by the raindrop is the same as the value calculated in part (a).