A student of weight 810 N was sent to another planet called Nerdland. If Nerdland has a mass that is 4 X the mass of the earth and a radius that is 1/2 the radius of the earth, what would be the mass in kg of the student when on Nerdland? what would be the weight in N of the student when on Nerdland?
mstudent = 810/9.81 = 82.6 kg
THE MASS, m in kg, DOES NOT CHANGE WITH g, ONLY THE WEIGHT
F = G * Mplanet* mstudent /r^2
on earth
810 = G Mearth * mstudent /rearth^2
on Nerdland
F = G Mnerd *82.6 / rnerd^2
so
F = G (4 Mearth) * 82.6 / (.25 rearth^2)
F = 16 G Mearth * 82.6 /rearth^2
or
16 * 810 = 12,960 Newtons
or in other words
half the radius -->4 g
then 4 times the earth mass --> another 4 times g
To determine the mass of the student on the planet Nerdland, we need to compare it to the mass of Earth.
Given:
Mass of Nerdland = 4 times the mass of Earth
Radius of Nerdland = 1/2 the radius of Earth
First, let's find the mass of Earth. The mass of Earth is approximately 5.972 × 10^24 kg.
Next, we can calculate the mass of Nerdland:
Mass of Nerdland = 4 * (Mass of Earth)
Mass of Nerdland = 4 * (5.972 × 10^24 kg)
Mass of Nerdland = 2.3888 × 10^25 kg
Therefore, the mass of the student on Nerdland would also be 2.3888 × 10^25 kg.
To calculate the weight of the student on Nerdland, we use the gravitational force equation:
Weight = Mass * gravity
where gravity is the acceleration due to gravity on a surface.
The acceleration due to gravity on Nerdland would depend on its radius. Since the radius is half that of Earth, the acceleration due to gravity would be twice that of Earth (since gravity is inversely proportional to the square of the distance).
Acceleration due to gravity on Nerdland = 2 * (Acceleration due to gravity on Earth)
Acceleration due to gravity on Nerdland = 2 * (9.8 m/s^2) = 19.6 m/s^2
Now, we can calculate the weight of the student on Nerdland:
Weight on Nerdland = Mass * Acceleration due to gravity on Nerdland
Weight on Nerdland = 2.3888 × 10^25 kg * 19.6 m/s^2
Therefore, the weight of the student on Nerdland would be 4.681 × 10^26 N.