Three real-world motion scenarios are described below.
Scenario I: A basketball is released from rest at a height of 2.4m above the floor and falls straight downward until it first contacts the floor.
Scenario II: A figure skater pulls her arms in while spinning about a vertical axis on essentially frictionless ice.
Scenario III: An automobile of length 4.5m travels at 12ms−1 around a flat curve of radius 25m. The curve is just tight enough that the driver must keep the wheels turned throughout the entire 90° turn.
Answer the following questions about the use of the object (point-mass) model for these motions.
(1) For each scenario, state whether treating the object as a point mass is appropriate for accurately predicting the quantities listed below. Support each choice with one clear, specific reason.
• Scenario I – Time from release to first contact with the floor
• Scenario II – Change in the skater’s angular speed after she pulls her arms in
• Scenario III – Net horizontal force required to keep the automobile moving along the curved path
(2) Based on your responses to part (a), articulate two general criteria that must be met before a real object may be modeled as a point mass when analyzing its motion.