Answer :
(a) The net gravitational force on the 34.0-kg object placed midway between the masses is zero.
(b) The 34.0-kg object can be placed at the midpoint between the two masses to experience a net force of zero.
(a) To find the net gravitational force exerted on the 34.0-kg object, we use Newton's law of universal gravitation:
[tex]\[ F = \frac{{G \cdot m_1 \cdot m_2}}{{r^2}} \][/tex]
Where:
- G is the gravitational constant [tex](\(6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2\))[/tex]
- [tex]\( m_1 \) and \( m_2 \)[/tex] are the masses of the two objects (235 kg and 535 kg, respectively)
- r is the separation between the objects (0.330 m)
The force exerted by each object on the 34.0-kg object is the same by Newton's third law, and since the objects are symmetrically placed, their forces cancel out.
Therefore, the net force on the 34.0-kg object is zero.
(b) To find the position where the net force on the 34.0-kg object is zero, we set up the equation for gravitational force and solve for the distance from the 535-kg mass where the gravitational force from each mass cancels out.
This position is the midpoint between the two masses.
