A body of mass m is attracted toward a 10.7 kg mass, 29.7 cm away, with a force of magnitude 6.54 10-8 N. Find m. Please Help!
F =G•m₁•m₂/R²
the gravitational constant G =6.67•10⁻¹¹ N•m²/kg²,
m₁ =10.7 kg
Sove for m₂
To solve this problem, we can use Newton's Law of Universal Gravitation, which states that the force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. We can express this relationship mathematically as:
F = G * (m1 * m2) / r^2
Where:
F is the force of attraction between two masses
G is the gravitational constant (approximately equal to 6.67430 x 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 force (F) is 6.54 x 10^-8 N, the distance (r) is 29.7 cm (which needs to be converted to meters), and one of the masses (m2) is 10.7 kg. We want to find the other mass (m1).
First, let's convert the distance from centimeters to meters:
r = 29.7 cm = 29.7/100 = 0.297 m
Next, we can rearrange the formula to solve for m1:
m1 = (F * r^2) / (G * m2)
Substituting the given values:
m1 = (6.54 x 10^-8 N * (0.297 m)^2) / (6.67430 x 10^-11 N m^2 / kg^2 * 10.7 kg)
m1 = (6.54 x 10^-8 N * 0.088209 m^2) / (7.128401 x 10^-9 N m^2 / kg)
Now, divide the numerator by the denominator to find the value of m1:
m1 ≈ 0.808 kg (to 3 significant figures)
Therefore, the mass of the body (m1) is approximately 0.808 kg.