Lead spheres of masses
1.7 kg and 20.4 g whose centers are separated
by 6.1 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
/kg2
.
Answer in units of N.
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6.67E-11*1.7*.0204/.061^2 =
6.2164902e-10
To calculate the gravitational force between the lead spheres, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the spheres,
G is the universal gravitational constant (6.67259 × 10^(-11) N·m^2/kg^2),
m1 and m2 are the masses of the spheres,
r is the distance between the centers of the two spheres.
Given:
m1 = 1.7 kg,
m2 = 20.4 g = 0.0204 kg,
r = 6.1 cm = 0.061 m.
Substituting these values into the formula:
F = (6.67259 × 10^(-11) N·m^2/kg^2 * 1.7 kg * 0.0204 kg) / (0.061 m)^2
F = (6.67259 × 10^(-11) N·m^2/kg^2 * 1.7 kg * 0.0204 kg) / 0.003721 m^2
F ≈ 1.772 N
Therefore, the gravitational force between the lead spheres is approximately 1.772 N.
To calculate the gravitational force between the lead spheres, we can use Newton's law of universal gravitation, which states that the force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The formula for calculating the gravitational force between two point masses is:
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 spheres, and
r is the distance between the centers of the spheres.
Given:
m1 = 1.7 kg (converted from grams to kilograms),
m2 = 20.4 g (converted from grams to kilograms),
r = 6.1 cm (converted from centimeters to meters),
G = 6.67259 × 10^(-11) N · m^2/kg^2.
Now, let's plug in the values into the formula to calculate the gravitational force:
F = (6.67259 × 10^(-11) N · m^2/kg^2) * (1.7 kg) * (20.4 g) / (0.061 m)^2.
First, convert 20.4 g to kilograms by dividing by 1000:
m2 = 20.4 g / 1000 = 0.0204 kg.
Now, calculate the distance in meters:
r = 6.1 cm / 100 = 0.061 m.
Plugging in the values:
F = (6.67259 × 10^(-11) N · m^2/kg^2) * (1.7 kg) * (0.0204 kg) / (0.061 m)^2.
Calculate the numerator:
Numerator = (6.67259 × 10^(-11) N · m^2/kg^2) * (1.7) * (0.0204) = 2.32624495328 × 10^(-12) N · m^2/kg.
Calculate the denominator:
Denominator = (0.061 m)^2 = 0.003721 m^2.
Now, divide the numerator by the denominator:
F = (2.32624495328 × 10^(-12) N · m^2/kg) / (0.003721 m^2).
Simplifying the equation:
F = 6.25244 × 10^(-10) N.
Therefore, the gravitational force between the two lead spheres is approximately 6.25244 × 10^(-10) N.