In introductory physics laboratories, a typical
Cavendish balance for measuring the gravitational constant G uses lead spheres of masses
1.27 kg and 18.4 g whose centers are separated
by 5.05 cm.
Calculate the gravitational force between
these spheres, treating each as a point mass
located at the center of the sphere. The
value of the universal gravitational constant
is 6.67259 × 10
−11
N · m2
/kg
2
.
Answer in units of N
Two balls, each with a mass of 0.803 kg,
exert a gravitational force of 8.27 × 10
−11
N
on each other.
How far apart are the balls? The value
of the universal gravitational constant is
6.673 × 10
−11
N m2
/kg
2
.
Answer in units of
To calculate the gravitational force between the two spheres, we can use Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the two masses,
G is the universal gravitational constant (6.67259 × 10^-11 N · m^2/kg^2),
m1 and m2 are the masses of the two spheres, and
r is the distance between their centers.
Given:
Mass of sphere 1 (m1) = 1.27 kg
Mass of sphere 2 (m2) = 18.4 g = 0.0184 kg
Distance between their centers (r) = 5.05 cm = 0.0505 m
Now, let's calculate the gravitational force:
F = (6.67259 × 10^-11 N · m^2/kg^2) * (1.27 kg) * (0.0184 kg) / (0.0505 m)^2
F = 1.07768 * 10^-8 N
Therefore, the gravitational force between the two spheres is approximately 1.07768 × 10^-8 N.