1.Two balls, each with a mass of 0.871 kg,
exert a gravitational force of 8.23 × 10−11 N
on each other.
How far apart are the balls? The value
of the universal gravitational constant is
6.673 × 10−11 Nm2/kg2.
Answer in units of m
I got .785 which is correct.
002 10.0 points
Mars has a mass of about 6.56 × 1023 kg,
and its moon Phobos has a mass of about
9.2 × 1015 kg.
If the magnitude of the gravitational force
between the two bodies is 4.68 × 1015 N,
how far apart are Mars and Phobos? The
value of the universal gravitational constant
is 6.673 × 10−11 N · m2/kg2.
Answer in units of m
Don't get this.
The answer is 9.37 × 10^6 m. To solve this, use the equation 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 bodies, and r is the distance between them. Rearrange the equation to solve for r, and plug in the given values.
To find the distance between two objects using the gravitational force, you can use the formula for Newton's law of gravitation:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force between the two objects,
G is the universal gravitational constant (6.673 × 10^-11 N·m^2/kg^2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
To find the distance, we rearrange the formula:
r = sqrt((G * (m1 * m2)) / F)
Let's apply this formula to the given problems:
Problem 1:
m1 = m2 = 0.871 kg
F = 8.23 × 10^-11 N
Substituting these values into the formula, we get:
r = sqrt((6.673 × 10^-11 N·m^2/kg^2 * (0.871 kg * 0.871 kg)) / (8.23 × 10^-11 N))
Simplifying the expression, we have:
r = sqrt(0.434 kg^2 * 10^2 / 8.23)
r = sqrt(5.027 / 8.23)
r = sqrt(0.609)
r ≈ 0.781 m
So the distance between the two balls is approximately 0.781 meters.
Problem 2:
m1 = 6.56 × 10^23 kg
m2 = 9.2 × 10^15 kg
F = 4.68 × 10^15 N
Substituting these values into the formula, we get:
r = sqrt((6.673 × 10^-11 N·m^2/kg^2 * (6.56 × 10^23 kg * 9.2 × 10^15 kg)) / (4.68 × 10^15 N))
Simplifying the expression, we have:
r = sqrt(6.13472 * 10^29)
r ≈ 7.83 × 10^14 m
So the distance between Mars and Phobos is approximately 7.83 × 10^14 meters.
To find the distance between Mars and Phobos, we can use the formula for the gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the magnitude of the gravitational force,
G is the universal gravitational constant (6.673 × 10^-11 N · m^2/kg^2),
m1 and m2 are the masses of the two objects,
and r is the distance between the two objects.
Given:
m1 = 6.56 × 10^23 kg
m2 = 9.2 × 10^15 kg
F = 4.68 × 10^15 N
G = 6.673 × 10^-11 N · m^2/kg^2
Let's plug in the values and solve for r:
4.68 × 10^15 = (6.673 × 10^-11 * 6.56 × 10^23 * 9.2 × 10^15) / r^2
Now, we can solve for r:
r^2 = (6.673 × 10^-11 * 6.56 × 10^23 * 9.2 × 10^15) / 4.68 × 10^15
r^2 = 75.408 × 10^22 / 4.68 × 10^15
r^2 = 16.11 × 10^7 m^2
Taking the square root of both sides:
r = sqrt(16.11 × 10^7 m^2)
r ≈ 401875.73 m
The distance between Mars and Phobos is approximately 401,875.73 meters.