Objects with masses of 105 kg and 528 kg
are separated by 0.482 m. A 41.1 kg mass is
placed midway between them.
0.482 m
b b
105 kg
41.1 kg
528 kg
Find the magnitude of the net gravitational
force exerted by the two larger masses on the
41.1 kg mass. The value of the universal gravitational constant is 6.672 × 10
−11
N · m2
/kg
2
.
Answer in units of N
Objects with masses of 105 kg and 528 kg
are separated by 0.482 m. A 41.1 kg mass is
placed midway between them.
0.482 m
b b
105 kg
41.1 kg
528 kg
Find the magnitude of the net gravitational
force exerted by the two larger masses on the
41.1 kg mass. The value of the universal gravitational constant is 6.672 × 10
−11
N · m2
/kg
2
F =G•m1•m2/R²
the gravitational constant G =6.67•10⁻¹¹ N•m²/kg²,
R= 0.241 m
F13= G•m1•m3/R²
F23= G•m2•m3/R²
F23-F13=
=G •m3• (m2-m1)/R²=
=6.67•10⁻¹¹•41.1•(528-105)/0.241²=…
To find the magnitude of the net gravitational force exerted by the two larger masses on the 41.1 kg mass, we can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force
G is the universal gravitational constant (6.672 × 10^-11 N · m^2/kg^2)
m1 and m2 are the masses of the two larger masses
r is the distance between the two masses
Given:
m1 = 105 kg
m2 = 528 kg
r = 0.482 m
First, we need to calculate the individual forces exerted by each of the larger masses on the 41.1 kg mass.
Force exerted by the 105 kg mass:
F1 = G * (m1 * m) / r^2
Substituting the values:
F1 = (6.672 × 10^-11 N · m^2/kg^2) * (105 kg * 41.1 kg) / (0.482 m)^2
Calculating F1:
F1 = (6.672 × 10^-11 N · m^2/kg^2) * (4315.5 kg^2) / (0.232324 m^2)
F1 = 6.672 × 10^-11 N · m^2/kg^2 * 186674.0481
F1 = 0.012441 N
Now, calculating the force exerted by the 528 kg mass:
F2 = G * (m2 * m) / r^2
Substituting the values:
F2 = (6.672 × 10^-11 N · m^2/kg^2) * (528 kg * 41.1 kg) / (0.482 m)^2
Calculating F2:
F2 = (6.672 × 10^-11 N · m^2/kg^2) * (21724.8 kg^2) / (0.232324 m^2)
F2 = 6.672 × 10^-11 N · m^2/kg^2 * 934634.1692
F2 = 0.062251 N
Since both forces are acting in the same direction towards the 41.1 kg mass, we can add them up to find the net gravitational force:
Net force = F1 + F2
Net force = 0.012441 N + 0.062251 N
Net force = 0.074692 N
Therefore, the magnitude of the net gravitational force exerted by the two larger masses on the 41.1 kg mass is 0.074692 N.
To find the magnitude of the net gravitational force exerted by the two larger masses on the 41.1 kg mass, we can use Newton's law of universal gravitation.
The formula for gravitational force 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 objects, and r is the distance between the centers of the two objects.
In this case, we have two larger masses of 105 kg and 528 kg, and the smaller mass is 41.1 kg. The distance between the two larger masses is given as 0.482 m.
First, we need to find the gravitational force between the two larger masses. Plugging the values into the formula:
F1 = (G * m1 * m2) / r^2
F1 = (6.672 x 10^-11 N * m^2 / kg^2) * (105 kg * 528 kg) / (0.482 m)^2
Now, we need to find the gravitational force between each of the larger masses and the small mass. Since the small mass is placed midway between the two larger masses, the distance between each larger mass and the small mass is half of the given distance, i.e., 0.482 m / 2 = 0.241 m.
Plugging the values into the formula for each larger mass:
F2 = (G * m1 * m3) / r^2
F2 = (6.672 x 10^-11 N * m^2 / kg^2) * (105 kg * 41.1 kg) / (0.241 m)^2
F3 = (G * m2 * m3) / r^2
F3 = (6.672 x 10^-11 N * m^2 / kg^2) * (528 kg * 41.1 kg) / (0.241 m)^2
Finally, we can find the net gravitational force by subtracting the forces between each larger mass and the small mass from the force between the two larger masses:
Net gravitational force = F1 - (F2 + F3)
Calculating these values will give you the magnitude of the net gravitational force exerted by the two larger masses on the 41.1 kg mass.