Gravitation Principles and Superposition Quiz

Gravitation and the Principle of Superposition

• Forces on a particle are considered, not forces on other particles
• Forces act on particle 1 due to particle 2 and 3, resulting in a net force
• Head-to-tail method demonstrates the net force vector on particle 1
• A different method also shows the net force through a head-to-tail arrangement
• A calculator's inverse tangent function can find the angle of the net force
• The correct angle is crucial for accurate calculations

Checkpoint 2

• The figure demonstrates four arrangements of three equal masses
• Rank the arrangements based on the net gravitational force on a specific mass, with the greatest force first
• Identify the direction of the net force in arrangement 2, either closer to a line of length d or D

Gravitation Near Earth's Surface

• Learning Objectives: Distinguish between free-fall acceleration and gravitational acceleration

• Learning Objectives: Calculate gravitational acceleration near a uniform, spherical body

• Learning Objectives: Differentiate between measured weight and gravitational force magnitude

• Gravitational acceleration at a distance from the Earth's center is calculated using F = GMm/r² and F = ma (ag = GM/r²)

• Table 13-1 illustrates the variation of ag with altitude

• Calculated acceleration values might differ slightly from measured values at locations

• Differences arise because Earth's mass isn't uniformly distributed, Earth isn't a perfect sphere, and Earth rotates

Difference in Gravitational Force and Weight Due to Rotation

• Centrifugal force is a key factor at the equator
• The normal force is upward, gravitational force downward.
• The net force is directed toward the Earth's center
• The object’s acceleration is related to both gravitational and centrifugal forces

Simulating Weightlessness

• Weightlessness can be simulated by ensuring that the object’s acceleration equals the gravitational acceleration
• This is achieved in a platform that moves with a specific angular velocity at a certain distance from the center.

Weighing a Fish in an Elevator

• The goal is to investigate how acceleration affects an object’s apparent weight
• Measured weight in an elevator at rest, during upward acceleration, downward acceleration, and during a cable break are analyzed
• Newton's second law is applied to the fish, considering the forces of the spring scale and gravity, to calculate the apparent weight
• An example calculation includes mass, gravitational acceleration, and acceleration of the elevator to determine the apparent weight.