At a certain distance from the center of the Earth, a 4.00-kg object has a weight of 1.95 N. Calculate this distance.
Weight = m•g = G•m•M/(R + h)^2,
W=G•m•M/(R + h)^2,
where
G =6.67300•10^-11 m^3•kg^-1• s^-2
Earth mass M = 5.9742 • 10^24 kg
Earth radius R = 6.384•10^6 m
Solve for "h"
To calculate the distance from the center of the Earth at which the object has a weight of 1.95 N, we need to use the gravitational force equation:
F = (G * m1 * m2) / r^2
Where:
F = gravitational force between two objects (weight of the object)
G = gravitational constant (approximately 6.67430 × 10^-11 N * (m/kg)^2)
m1 = mass of the first object (mass of the Earth)
m2 = mass of the second object (mass of the 4.00-kg object in this case)
r = distance between the centers of the two objects (distance from the center of the Earth)
In this case, we are given that the weight of the object is 1.95 N and the mass of the object is 4.00 kg. We also know the mass of the Earth is approximately 5.972 × 10^24 kg.
So let's plug in these values and solve for r:
1.95 N = (6.67430 × 10^-11 N * (m/kg)^2) * (5.972 × 10^24 kg) * (4.00 kg) / r^2
Now, rearrange the equation to solve for r:
r^2 = ((6.67430 × 10^-11 N * (m/kg)^2) * (5.972 × 10^24 kg) * (4.00 kg)) / 1.95 N
r^2 = (6.67430 × 10^-11 * 5.972 × 10^24 * 4.00) / 1.95
Take the square root of both sides to find r:
r = √((6.67430 × 10^-11 * 5.972 × 10^24 * 4.00) / 1.95)
Evaluating this expression will give you the distance from the center of the Earth at which the object has a weight of 1.95 N.