What is the mass of m2 when m1=860 kg, the centers of the masses are 2.4 meters apart, and the magnitude of the gravitational force on each mass is 9.07×10−6 N?
Please check my answer
m2=910 kg***
m2=91 kg
m2=107 kg
m2=810 kg
looks good
Well, if the magnitude of the gravitational force on each mass is 9.07×10−6 N, then we can use Newton's law of universal gravitation to find the mass of m2. According to this law, the gravitational force between two objects can be calculated using the equation F = (G * m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
Solving for m2 in this equation, we get m2 = (F * r^2) / (G * m1). Plugging in the given values, we have m2 = (9.07×10−6 N * (2.4 m)^2) / (G * 860 kg).
Now, we could go into the details of calculating the gravitational constant and crunching the numbers, but that wouldn't be much fun, would it? How about I tell you the answer in a much more entertaining way?
Drumroll, please...
The mass of m2 is approximately 910 kg! Ta-da! Now you have an answer and a smile on your face.
To find the mass of m2, we can use the formula for gravitational force:
F = G * (m1 * m2) / r^2,
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.
In this case, we are given:
m1 = 860 kg,
F = 9.07×10^(-6) N,
r = 2.4 meters.
Rearranging the formula, we can solve for m2:
m2 = (F * r^2) / (G * m1).
Plugging in the given values:
m2 = (9.07×10^(-6) N * (2.4 meters)^2) / (G * 860 kg).
Now, we need the value of the gravitational constant: G = 6.67430 × 10^(-11) N m^2 / kg^2.
m2 = (9.07×10^(-6) N * (2.4 meters)^2) / (6.67430 × 10^(-11) N m^2 / kg^2 * 860 kg).
Simplifying:
m2 = (0.04905408 N * meters^2) / (5.732X10^(-8) N m / kg).
Dividing the units:
m2 = (0.04905408 N * meters^2 * kg) / (5.732X10^(-8) N m).
Canceling the units:
m2 = (0.04905408 kg * meters^2) / (5.732X10^(-8) m).
Calculating:
m2 ≈ 0.85304 × 10^6 kg.
Therefore, the mass of m2 is approximately 0.853 × 10^6 kg.
To find the mass of m2, we can use Newton's law of universal gravitation formula:
F = (G * m1 * m2) / r^2
Where:
F is the magnitude of the gravitational force,
G is the gravitational constant (6.67430 × 10^-11 N m^2 / kg^2),
m1 is the mass of the first object (860 kg),
m2 is the mass of the second object (which we are trying to find),
and r is the distance between the centers of the masses (2.4 meters).
In this case, the magnitude of the gravitational force is given as 9.07 × 10^-6 N.
We can rearrange the formula to solve for m2:
m2 = (F * r^2) / (G * m1)
Substituting the given values into the equation:
m2 = (9.07 × 10^-6 N * (2.4 m)^2) / ((6.67430 × 10^-11 N m^2 / kg^2) * 860 kg)
m2 = (9.07 × 10^-6 N * 5.76 m^2) / (5.748198 × 10^-8 N m^2 / kg)
m2 ≈ 9.07 × 10^-6 N * 5.76 m^2 * (1 / 5.748198 × 10^-8 N m^2 / kg)
m2 ≈ 910 kg
Therefore, the correct answer is m2 = 910 kg.