if Royce was 10 years old and he had a mass of 30kg. but by the time he turned 16 his mass has grown to 60kg. how much larger is the gravitational force between Royce and earth at age 16 compared to age 10

To find out how much larger the gravitational force is between Royce and the Earth at age 16 compared to age 10, we can use the equation for gravitational force:

F = G * (m1 * m2) / r^2

Where:
F is the gravitational force
G is the gravitational constant (approximately 6.674 * 10^-11 N*m^2 / kg^2)
m1 is the mass of Royce at age 10 (30 kg)
m2 is the mass of the Earth (approximately 5.972 × 10^24 kg)
r is the distance between Royce and the center of the Earth (approximately the radius of the Earth, 6,371 km)

Let's calculate the gravitational force at age 10 first:

F1 = G * (m1 * m2) / r^2

And then calculate the gravitational force at age 16:

F2 = G * (m2 * m2) / r^2

Finally, we can find the ratio of the two forces, which will tell us how much larger the gravitational force is at age 16 compared to age 10:

Ratio = F2 / F1

Let's plug in the values and calculate it step-by-step:

Step 1: Calculate the gravitational force at age 10

F1 = (6.674 * 10^-11 N*m^2 / kg^2) * (30 kg * (5.972 × 10^24 kg)) / (6,371 km)^2

Step 2: Calculate the gravitational force at age 16

F2 = (6.674 * 10^-11 N*m^2 / kg^2) * (60 kg * (5.972 × 10^24 kg)) / (6,371 km)^2

Step 3: Calculate the ratio

Ratio = F2 / F1

To determine the change in gravitational force between Royce and Earth at age 16 compared to age 10, we need to understand the relationship between gravitational force and mass.

The gravitational force between two objects can be calculated using the formula:

F = G * (m1 * m2) / r^2

Where:
- F is the gravitational force between the objects.
- G is the gravitational constant (approximately equal to 6.674 × 10^(-11) N·m^2/kg^2).
- m1 and m2 are the masses of the two objects.
- r is the distance between the centers of the two objects.

In this case, one of the objects is Earth, which we can assume has a constant mass and radius. Therefore, the only factor changing is Royce's mass.

At age 10, Royce's mass is 30 kg. Let's call this m1.
At age 16, Royce's mass is 60 kg. Let's call this m2.

The gravitational force at age 10 is given by:
F1 = G * (m1 * MEarth) / r^2

The gravitational force at age 16 is given by:
F2 = G * (m2 * MEarth) / r^2

To find the difference between the two forces, we subtract F1 from F2:
ΔF = F2 - F1

Let's calculate the values.

First, we need to determine the difference in mass:
Δm = m2 - m1 = 60 kg - 30 kg = 30 kg

Now, we can calculate the difference in gravitational force using the formula:
ΔF = G * (Δm * MEarth) / r^2

Substituting the known values:
ΔF = 6.674 × 10^(-11) N·m^2/kg^2 * (30 kg * MEarth) / r^2

Please note that the actual value of the gravitational force change depends on the distance between Royce and Earth (r) and the mass of Earth (MEarth). These values are not provided in the question, so we cannot calculate the exact numerical answer. However, by following the steps above, you should be able to calculate the answer once the necessary values are known.

That force equals his weight. Since it is proportional to his mass (times g), his weight doubles during that six year interval.

g remains constant.

2 times larger