Tom has a mass of 69.0 kg and Sally has a mass of 54.0 kg. Tom and Sally are standing 20.0 m apart on the dance floor. Sally looks up and sees Tom. She feels an attraction. If the attraction is gravitational, find its size. Assume that both Tom and Sally can be replaced by spherical masses. (Use G = 6.67 10-11 N · m2/kg2.)
F =G•m1•m2/R²
the gravitational constant G =6.67•10⁻¹¹ N•m²/kg²,
6.213105e-10
To find the gravitational attraction between Tom and Sally, we can use Newton's law of gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the two masses,
G is the gravitational constant (G = 6.67 * 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 their masses.
In this case, Tom's mass (m1) is 69.0 kg, Sally's mass (m2) is 54.0 kg, and the distance between them (r) is 20.0 m.
Substituting these values into the equation, we get:
F = (6.67 * 10^-11 N · m^2/kg^2) * (69.0 kg) * (54.0 kg) / (20.0 m)^2
F = (0.0000000000667 N · m^2/kg^2) * (3735 kg^2) / (400 m^2)
F = 0.0000000000667 N · m^2 / 149.5 m^2
F = 4.4545 * 10^-13 N
Therefore, the size of the gravitational attraction between Tom and Sally is approximately 4.4545 * 10^-13 Newtons.