You are an explorer on a tiny planet with no atmosphere. You drop a coffee filter and find that it falls 2.0m in 1.6s. As you were approaching the planet, you measured the radius to be 1.8x10^6 m. What is the mass of the planet?
So I used the 2.0m and 1.6s to figure out the acceleration due to gravity of the planet (I got 0.781 m/s^2). Under the assumption that it's velocity went from 0 to 1.25m/s in 1.6s (I got the velocity by dividing the distance by the time). Also since there's no air resistance I didn't need to worry about that affecting the acceleration.
But, I'm a little lost on how to figure out the mass of the planet without the mass of the coffee filter or the force acting upon the coffee filter.
I thought i could use F= G(m1)(m2)/(absolute value r)^2
with d being the radius but what do I do if I don't know the masses or the force involved?
To determine the mass of the planet, you can use the concept of gravitational acceleration and Newton's law of universal gravitation.
First, you correctly calculated the acceleration due to gravity on the planet using the information provided: 0.781 m/s^2.
Now, let's consider the relationship between gravitational acceleration, mass, and radius. The equation for gravitational acceleration is given by:
g = G * (M / r^2),
where g is the gravitational acceleration, G is the universal gravitational constant (approximately 6.67 x 10^-11 N·m^2/kg^2), M is the mass of the planet, and r is the radius of the planet.
Since you measured the radius of the planet to be 1.8 x 10^6 m, you have all the necessary information to solve for the mass of the planet (M).
Rearranging the equation, we get:
M = (g * r^2) / G.
Substituting the values, we have:
M = (0.781 m/s^2 * (1.8 x 10^6 m)^2) / (6.67 x 10^-11 N·m^2/kg^2).
Calculating this expression will yield the mass of the planet.
Remember to pay attention to unit conversions and make sure all units are consistent in order to obtain correct results.