Answer :
(a) To find the magnitude of the net gravitational force exerted by the 195 kg and 495 kg objects on the 51.0 kg object, we can use the equation for gravitational force:
- F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.67430 x 10^-11 N m^2/kg^2), m1 and m2 are the masses of the objects, and r is the distance between their centers.
Given:
- m1 = 195 kg
- m2 = 495 kg
- r = 3.40 m
Substituting these values into the equation, we have:
- F = (6.67430 x 10^-11 N m^2/kg^2) * (195 kg * 495 kg) / (3.40 m)^2
Calculating this expression gives us the magnitude of the net gravitational force.
(b) To find the position where the 51.0 kg object can experience a net force of zero from the other two objects, we need to find the point where the gravitational forces exerted by the two objects cancel each other out.
Let's assume the 195 kg object is located at the origin (0 m) and the 495 kg object is at a position x from the origin, towards the 195 kg object. The gravitational force exerted by the 195 kg object on the 51.0 kg object is directed towards the origin, while the force exerted by the 495 kg object is directed away from the origin.
To find the position x where the net force is zero, we can equate the magnitudes of these two forces:
- F1 = F2
- G * (195 kg * 51.0 kg) / x^2 = G * (495 kg * 51.0 kg) / (3.40 m - x)^2
Simplifying and solving this equation will give us the position x where the net force is zero.
Please note that for a complete solution, specific numerical values and calculations are necessary.
About gravitational force
Gravitational force refers to the attractive force between two objects with mass. It is one of the fundamental forces of nature and is described by Newton's law of universal gravitation. The gravitational force is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between their centers. Its magnitude can be calculated using the equation:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2/kg^2), m1 and m2 are the masses of the objects, and r is the distance between their centers. The gravitational force is always attractive, meaning it pulls objects toward each other.
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