If You weigh 690 N.
What would you weigh if the Earth were six
times as massive as it is and its radius were
four times its present value?
Answer in units of N.
Need help i don't know how this
your weight (gravitational attraction to the Earth)
... is directly proportional to the product of the masses (you and Earth)
... and is inversely proportional to the square of the distance between the centers of mass
690 N * 6 / (4^2)
you have to figure the new radius, which is 4R.
Notice weight= constant*Mass/(R^2)
so witth the change, M is now 6M, , and R^2 becomes (4R)^2 or 16R^2
so as I see it, weight is now original weight*6/16
To calculate your weight on the Earth if it were six times as massive and its radius were four times its current value, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
Assuming your weight of 690 N is due to the gravitational force between you and the Earth, we can consider the Earth as one of the objects in the formula.
Let's denote the current mass of the Earth as m_current and the current radius as r_current.
According to the problem, the Earth is six times as massive, so the new mass of the Earth (m_new) would be:
m_new = 6 * m_current
The radius of the Earth is four times its present value, so the new radius (r_new) would be:
r_new = 4 * r_current
We don't need to know the actual values of G, m_current, or r_current to find the change in your weight. We can express the ratio of the gravitational forces using the formula:
F_new / F_current = (m_new / m_current) * (r_current / r_new)^2
Plugging in the values we know:
F_new / 690 N = (6 * m_current / m_current) * (r_current / (4 * r_current))^2
Simplifying:
F_new / 690 N = 6 * (1 / 4)^2
F_new / 690 N = 6 * (1 / 16)
F_new / 690 N = 6 / 16
F_new / 690 N = 3 / 8
To find the new weight (F_new), we can set up a proportion:
F_new / 690 N = 3 / 8
Cross-multiplying:
8 * F_new = 690 * 3
Dividing both sides by 8:
F_new = (690 * 3) / 8
F_new = 2070 / 8
F_new = 258.75 N
Therefore, if the Earth were six times as massive as it is right now and its radius were four times its present value, you would weigh approximately 258.75 N.
To find out what you would weigh if the Earth were six times as massive as it is and its radius were four times its present value, we need to use the Law of Universal Gravitation. The formula for calculating weight (W) is given by:
W = (G * m1 * m2) / r^2
Where:
- G is the gravitational constant
- m1 is the mass of the object (in this case, your weight)
- m2 is the mass of the Earth
- r is the distance between the center of the object and the center of the Earth (in this case, the Earth's radius)
Given that your weight is 690 N, we can substitute this value in the formula:
690 = (G * m1 * m2) / r^2
Now, let's look at the changes in the scenario:
1. The mass of the Earth is six times as massive as it is currently.
2. The radius of the Earth is four times its present value.
Let's assign the current values:
- Mass of the Earth (m2) = current mass
- Radius of the Earth (r) = current radius
Now, let's assign the changed values:
- Mass of the Earth (m2) = 6 * current mass
- Radius of the Earth (r) = 4 * current radius
Substituting these values into the equation:
690 = (G * m1 * (6 * current mass)) / (4 * current radius)^2
To simplify the equation, we can cancel out common factors and rearrange it:
690 * (4 * current radius)^2 = G * m1 * (6 * current mass)
Now, we need the values for the gravitational constant (G), the current radius, and the current mass. The gravitational constant is approximately 6.674 × 10^-11 N m^2/kg^2.
You will need to find and substitute the current radius and current mass values into the equation. With all the required values, you can now solve the equation to find the new weight.