A student of weight 830 N was sent to another planet called Nerdland. If Nerdland has a mass that is three times the mass of the earth and a radius that is half the radius of the earth, what would be the mass in kg of the student when on Nerdland?
The change in Wt. that you experience when on a different planet is not caused by a change in your mass. Your
mass is constant. The change in wt. is
caused by the change in gravity(g).
To calculate the mass of the student on Nerdland, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
where F is the weight (830 N in this case), G is the gravitational constant (approximately 6.674 × 10^-11 N m^2 / kg^2), m1 is the mass of the student, m2 is the mass of Nerdland, and r is the radius of Nerdland.
First, we need to calculate the mass of Nerdland. Given that Nerdland has three times the mass of the earth, we can use the equation:
m2 = 3 * mE
where mE is the mass of the Earth (approximately 5.972 × 10^24 kg).
Next, we need to calculate the radius of Nerdland. Given that the radius of Nerdland is half the radius of the earth, we can use the equation:
r = rE / 2
where rE is the radius of the Earth (approximately 6,371 km or 6.371 × 10^6 m).
Now we can substitute the values into the gravitational force formula to solve for the mass of the student:
830 N = (6.674 × 10^-11 N m^2 / kg^2) * m1 * (3 * 5.972 × 10^24 kg) / ((6.371 × 10^6 m / 2)^2)
Simplifying the equation and solving for m1, the mass of the student on Nerdland, we get:
m1 = (830 N * (6.371 × 10^6 m)^2) / (6.674 × 10^-11 N m^2 / kg^2 * 3 * 5.972 × 10^24 kg)
Plugging in the values, we can calculate the mass of the student on Nerdland.