A 3.3 kg mass weighs 30.03 N on the surface
of a planet similar to Earth. The radius of
this planet is roughly 7.4 × 106 m.
Calculate the mass of of this planet. The
value of the universal gravitational constant
is 6.67259 × 10−11 N · m2/kg2.
Answer in units of kg
Solve this equation for M:
30.03 = G M*m/R^2
= G * M*3.3/(7.4*10^6)^2
where G is the universal graitational constant, 6.67^10^-11.
You should only keep two or three significant figures in the answer, since they have only given you a "rough" R value.
Sure! Let me calculate that for you using my stellar comedic skills. *Drumroll, please!*
To find the mass of the planet, we can use the formula for gravitational force:
F = (G * M * m) / r^2,
where F is the weight of the mass (30.03 N), G is the gravitational constant (6.67259 × 10−11 N · m2/kg2), M is the mass of the planet (what we're trying to find), m is the mass of the object (3.3 kg), and r is the radius of the planet (7.4 × 10^6 m).
Now, let's put on our math clown shoes and solve for M:
M = (F * r^2) / (G * m).
Plugging in the values, we get:
M = (30.03 N * (7.4 × 10^6 m)^2) / (6.67259 × 10−11 N · m2/kg2 * 3.3 kg).
Calculating that out, my comedic calculator gives me the answer:
M ≈ 2.4451 × 10^24 kg.
So, the mass of the planet is approximately 2.4451 × 10^24 kg. Ta-da!
To calculate the mass of the planet, we can use the equation for gravitational force:
F = (G * m1 * m2) / r^2
Where:
- F is the gravitational force between two objects
- G is the universal gravitational constant (6.67259 × 10^(-11) N·m^2/kg^2)
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects
In this case, we know the weight of the mass on the surface of the planet, which is equal to the gravitational force. So we can rewrite the equation as follows:
30.03 N = (G * m * planet_mass) / planet_radius^2
Given:
- Mass of the object: 3.3 kg
- Weight of the object: 30.03 N
- Radius of the planet: 7.4 × 10^6 m
- Universal gravitational constant: 6.67259 × 10^(-11) N·m^2/kg^2
We can rearrange the equation to solve for the mass of the planet.
First, let's isolate the planet mass:
30.03 N * planet_radius^2 = G * m * planet_mass
Now, rearrange to solve for planet_mass:
planet_mass = (30.03 N * planet_radius^2) / (G * m)
Substituting the given values into the equation:
planet_mass = (30.03 N * (7.4 × 10^6 m)^2) / (6.67259 × 10^(-11) N·m^2/kg^2 * 3.3 kg)
Calculating this value, we find:
planet_mass = 1.92261908715 × 10^24 kg
Therefore, the mass of the planet is approximately 1.92 × 10^24 kg.
To calculate the mass of the planet, we can use the formula for the gravitational force between two objects:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the universal gravitational constant
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
In this case, we have the weight of the mass on the surface of the planet (30.03 N) and the mass of the object (3.3 kg). We can use the weight of the mass as the gravitational force. Since the mass of the planet (m2) is what we are trying to find, we rearrange the formula as follows:
m2 = (F * r^2) / (G * m1)
Substituting the given values into the equation:
m2 = (30.03 N * (7.4 × 10^6 m)^2) / (6.67259 × 10^(-11) N · m^2/kg^2) / 3.3 kg
Calculating this equation will give us the mass of the planet.