Gravitational Forces and Fields

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- This standard is part of: P.F.CE.2

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A scale indicates weight by measuring the normal force between the object and the surface supporting it. The reading on the scale accurately measures the weight if the system is not accelerating and the net force is zero. However, if the scale is used in an accelerating system as in an elevator, the reading on the scale does not equal the actual weight. The scale reading can be referred to as the “apparent weight.” This apparent weight in accelerating elevators can be explained and calculated using force diagrams and Newton’s laws.

The strength of an object’s (i.e., the source’ s) gravitational field at a certain location, g, is given by the gravitational force per unit of mass experienced by another object placed at that location, g = Fg/m. Comparing this equation to Newton’s second law can be used to explain why all objects on Earth’s surface accelerate at the same rate in the absence of air resistance. While the gravitational force from another object can be used to determine the field strength at a particular location, the field of the object is always there, even if the object is not interacting with anything else. The field direction is toward the center of the source. Given the gravitational field strength at a certain location, the gravitational force between the source of that field and any object at that location can be calculated. Greater gravitational field strengths result in larger gravitational forces on masses placed in the field. Gravitational fields can be represented by field diagrams obtained by plotting field arrows at a series of locations. Field line diagrams are excluded from this course. Distinctions between gravitational and inertial masses are excluded.

Gravitational interactions are very weak compared to other interactions and are difficult to observe unless one of the objects is extremely massive (e.g., the sun, planets, moons). The force law for gravitational interaction states that the strength of the gravitational force is proportional to the product of the two masses and inversely proportional to the square of the distance between the centers of the masses Fg = ((G x m₁ × m₂)/r²). The proportionality constant, G, is called the universal gravitational constant. Problem solving may involve calculating the net force for an object between two massive objects (e.g., Earth-moon system, planet-sun system) or calculating the position of such an object given the net force.