Answer :
The gravitational force F between the masses is approximately [tex]\( 5.94 \times 10^{-13} \text{ N} \)[/tex].
To find the gravitational force F between two masses, we can use the formula:
[tex]\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \][/tex]
where:
- G is the gravitational constant, [tex]\( 6.67 \times 10^{-11} \)[/tex] N·m²/kg²
- [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] are the masses of the objects in kg
- [tex]\( r \)[/tex] is the distance between the centers of the masses in meters
Given:
- [tex]\( m_1 = 92.0 \)[/tex] kg
- [tex]\( m_2 = 0.894 \)[/tex] kg
- [tex]\( r = 99.3 \)[/tex] m
- [tex]\( G = 6.67 \times 10^{-11} \)[/tex] N·m²/kg²
First, calculate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = (99.3 \text{ m})^2 \][/tex]
[tex]\[ r^2 = 9860.49 \text{ m}^2 \][/tex]
Now, calculate the gravitational force [tex]\( F \)[/tex]:
[tex]\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \][/tex]
[tex]\[ F = \frac{6.67 \times 10^{-11} \times 92.0 \times 0.894}{9860.49} \][/tex]
[tex]\[ F = \frac{5.8628 \times 10^{-9}}{9860.49} \][/tex]
[tex]\[ F \approx 5.94 \times 10^{-13} \text{ N} \][/tex]
Therefore, the gravitational force F between the masses is approximately [tex]\( 5.94 \times 10^{-13} \text{ N} \)[/tex].
Complete Question:
What is the gravitational force between mass 1 (92.0 kg) and mass 2 (0.894 kg) when they are 99.3 m apart? Given that [tex]\( G = 6.67 \times 10^{-11} \)[/tex] N·m²/kg², express the answer in the form [tex]\( F = [?] \times 10^x \)[/tex] N.
To calculate the gravitational force between two masses, you use the formula F = G * (m1 * m2) / d^2. Substituting in the given values of the two masses and the distance between them, the gravitational force is found to be 5.53 * 10^-7 Newtons.
The question is asking to calculate the gravitational force between two masses using Newton's law of universal gravitation. This law states that the gravitational force (F) between two masses is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (d) between them, represented by the formula:
F = G * (m1 * m2) / d^2
Given values:
- Mass 1 (m1) = 92.0 kg
- Mass 2 (m2) = 0.894 kg
- Distance (d) = 99.3 m
- Gravitational constant (G) = 6.67 * 10^-11 Nm^2/kg^2
To find the gravitational force, we substitute these values into the formula:
F = (6.67 * 10^-11 Nm^2/kg^2) * (92.0 kg * 0.894 kg) / (99.3 m)^2
After performing the calculations:
F = (6.67 * 10^-11) * (82.288) / (9859.29)
F = 5.53 * 10^-7 N
Therefore, the gravitational force between the two masses is 5.53 * 10^-7 Newtons.
