a 500g balance weight is transported to the surface of planet z where an objects weight is measured to be 5.00N. The radius of the planet is 5.0x10^5m. What is the mass of planet z?
well,
F = GMm/r^2
5.00 = GM(0.5)/(5.0*10^5)^2
Plug in G and solve for M
To find the mass of planet Z, we can use the formula for gravitational force:
F = (GMm)/r^2
Where:
- F is the gravitational force between two objects
- G is the gravitational constant (approximately 6.674 × 10^-11 m^3 kg^-1 s^-2)
- M is the mass of planet Z
- m is the mass of the object
- r is the radius of planet Z
First, let's convert the weight of the 500g weight to kilograms:
Weight = mass x acceleration due to gravity
5.00N = 0.500kg x 9.8 m/s^2
Now, let's calculate the gravitational force between the object (500g weight) and the planet (mass M):
F = (GMm)/r^2
Rearranging the formula to solve for M:
M = (Fr^2)/(Gm)
Substituting the given values:
M = (5.00N x (5.0x10^5m)^2)/(6.674 × 10^-11 m^3 kg^-1 s^-2 x 0.500kg)
Now, let's perform the calculation to determine the mass of planet Z:
M = (5.00N x 2.5x10^11m^2) / (3.337 × 10^-11 m^3 kg^-1 s^-2 x 0.500kg)
M = (12.5x10^11 N·m) / (1.6685 × 10^-11 N·m^2 / kg)
M = 12.5x10^11 N·m x kg / 1.6685x10^11 N·m^2
M = 7.5kg
Therefore, the mass of planet Z is approximately 7.5kg.