A raindrop has a mass of 5.9 10-7 kg and is falling near the surface of the earth. Calculate the magnitude of the gravitational force exerted in the following.
(a) on the raindrop by the earth
To calculate the magnitude of the gravitational force exerted on the raindrop by the Earth, we can use Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2),
m1 is the mass of the raindrop,
m2 is the mass of the Earth, and
r is the distance between the centers of the raindrop and the Earth.
In this case, we know the mass of the raindrop (m1 = 5.9 * 10^-7 kg). The mass of the Earth (m2) is approximately 5.972 × 10^24 kg, and since the raindrop is falling near the surface of the Earth, we can assume the distance (r) between the centers of the raindrop and Earth is approximately equal to the radius of the Earth, which is approximately 6,371 km or 6.371 × 10^6 meters.
Now, let's calculate the magnitude of the gravitational force:
F = (6.67430 × 10^-11 N(m/kg)^2) * (5.9 × 10^-7 kg) * (5.972 × 10^24 kg) / (6.371 × 10^6 m)^2
F ≈ 4.90 × 10^-5 N
Therefore, the magnitude of the gravitational force exerted on the raindrop by the Earth is approximately 4.90 × 10^-5 Newtons.