Joe has a weight of 850 N (about 193 lb) when he is standing on the surface of the Earth. What would his weight (the gravitational force due to the Earth) be if he tripled his distance from the center of the Earth by flying in a spacecraft?

Take the weight and divide it by 9.

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If Joe tripled his distance from the center of the Earth by flying in a spacecraft, his weight would certainly be out of this world! It would decrease because the gravitational force decreases as you move further away from the center of the Earth. But don't worry, Joe won't be left feeling weightless like an astronaut in space. Just slightly lighter than before! So, let's do some calculations.

Since weight is directly proportional to the gravitational force, we can use the inverse square law of gravity. According to this law, the gravitational force decreases as the square of the distance from the center of the Earth increases.

Let's assume Joe's initial distance from the center of the Earth is D, and after tripling that distance it becomes 3D.

Using the inverse square law of gravity, we can say that the weight (W) is inversely proportional to the square of the distance (D):

W1/D1^2 = W2/D2^2

Where:
W1 is the initial weight of Joe (850 N),
D1 is the initial distance from the center of the Earth,
W2 is the weight we need to find, and
D2 is the new distance from the center of the Earth (3D).

Let's plug in the values and solve:

850 N / D1^2 = W2 / (3D)^2

850 N / D1^2 = W2 / 9D^2

Cross-multiplying gives us:

W2 = 9 * 850 N

W2 = 7,650 N

So, if Joe tripled his distance from the center of the Earth, his weight would be approximately 7,650 N. That's lighter on the scale, but still heavy on the humor!

To find out Joe's weight if he tripled his distance from the center of the Earth, we need to use the gravitational force formula.

The formula to calculate 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/kg)^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the two objects.

In this case, we need to calculate the change in gravitational force when Joe triples his distance from the center of the Earth. Let's assume that Joe's mass remains the same.

Initially, Joe's weight on the surface of the Earth is 850 N. Since weight is the force due to gravity, we can say that Joe's mass is 850 N divided by the acceleration due to gravity (g ≈ 9.8 m/s^2).

So, Joe's initial mass is 850 N / 9.8 m/s^2 ≈ 86.7 kg.

When Joe triples his distance from the center of the Earth, the new distance (r) becomes three times the original distance. Since distance from the center of the Earth determines gravity, we can say that the new gravitational force will be inversely proportional to the square of the new distance.

Using the formula, we can calculate the new gravitational force (F_new):
F_new = G * m1 * m2 / (3r)^2

Substituting the values, we get:
F_new = G * m1 * m2 / (9 * r^2)

To find the new weight (the gravitational force), we multiply the mass (m1) by the new acceleration due to gravity (g_new):
Weight_new = m1 * g_new

Now, we need to find g_new:
g_new = G * m2 / (3r)^2

Substituting the values, we get:
g_new = G * m2 / (9 * r^2)

Finally, substituting g_new in the equation for Weight_new, we get:
Weight_new = m1 * (G * m2 / (9 * r^2))

By substituting the known values of m1, G, m2, and r, we can calculate the new weight.

850N/(3r)^2= 850/9r^2=94.4 Newtons