1) Find the magnitude of the gravitational force
a 68.6 kg person would experience while
standing on the surface of Earth with a
mass of 5.98 × 10
24
kg and a radius of
6.37 × 10
6
m. The universal gravitational
constant is 6.673 × 10
−11
N · m2
/kg
2
.
Answer in units of N
2) Find the magnitude of the gravitational force
on Mars, with a mass of 6.34 × 10
23
kg and a
radius of 3.43 × 10
6 m.
Answer in units of N
3) Find the magnitude of the gravitational force
on Pluto, with a mass of 1.32 × 10
22
kg and a
radius of 1.15 × 10
6 m.
Answer in units of N
ccd
To find the magnitude of the gravitational force, you can use the formula:
F = (G * (m1 * m2)) / r^2
where:
F is the gravitational force
G is the universal gravitational constant (6.673 × 10^-11 N · m^2 / kg^2)
m1 is the mass of the first object
m2 is the mass of the second object
r is the distance between the two objects (radius in this case)
Let's go through each question to find the answers:
1) Find the magnitude of the gravitational force a 68.6 kg person would experience while standing on the surface of Earth with a mass of 5.98 × 10^24 kg and a radius of 6.37 × 10^6 m.
First, we need to plug in the values into the formula:
F = (6.673 × 10^-11 N · m^2 / kg^2) * ((68.6 kg) * (5.98 × 10^24 kg)) / (6.37 × 10^6 m)^2
Now, calculate the answer:
F = (6.673 × 10^-11 N · m^2 / kg^2) * (3.89908 × 10^26 kg) / (4.06769 × 10^13 m^2)
F ≈ 6.08 × 10^14 N
So, the magnitude of the gravitational force on a 68.6 kg person standing on the surface of Earth is approximately 6.08 × 10^14 N.
2) Find the magnitude of the gravitational force on Mars, with a mass of 6.34 × 10^23 kg and a radius of 3.43 × 10^6 m.
Using the same formula as before:
F = (6.673 × 10^-11 N · m^2 / kg^2) * ((6.34 × 10^23 kg) * (5.98 × 10^24 kg)) / (3.43 × 10^6 m)^2
Calculating the answer:
F = (6.673 × 10^-11 N · m^2 / kg^2) * (3.78932 × 10^48 kg) / (1.17649 × 10^13 m^2)
F ≈ 1.62 × 10^16 N
Therefore, the magnitude of the gravitational force on Mars is approximately 1.62 × 10^16 N.
3) Find the magnitude of the gravitational force on Pluto, with a mass of 1.32 × 10^22 kg and a radius of 1.15 × 10^6 m.
Using the same formula as before:
F = (6.673 × 10^-11 N · m^2 / kg^2) * ((1.32 × 10^22 kg) * (5.98 × 10^24 kg)) / (1.15 × 10^6 m)^2
Calculating the answer:
F = (6.673 × 10^-11 N · m^2 / kg^2) * (7.89736 × 10^46 kg) / (1.3225 × 10^12 m^2)
F ≈ 4.71 × 10^17 N
Hence, the magnitude of the gravitational force on Pluto is approximately 4.71 × 10^17 N.