Augustana College Physics Laboratories

Hanson Hall of Science, Rock Island, IL

Free Fall

Goals

  • Analyze motion of a falling object from a video
  • Measure acceleration of gravity by tracking the motion of a falling object
  • Track the motion of a falling object that experiences significant drag and measure the effect of air resistance on the object’s acceleration

Resources/Guides

Background

Near the surface of the earth, we can model the force of gravity quite well by assuming that it has a constant acceleration, independent of height. This does not hold far from Earth’s surface, where the force of gravity decreases proportionally to the square of the distance from the center of the planet.

Assuming constant acceleration g, t seconds after an object is released from a height h it will have a height y and velocity v_y given by y=h-\tfrac{1}{2}gt^2

and v_y=-gt

respectively.

The acceleration of gravity near Earth’s surface is determined experimentally, and varies from place to place because of the non-spherical shape of the earth and differing composition of its crust. In the lab at Augustana, the accepted value is 9.8025 m/s2. The measured value of the acceleration of gravity at the surface of the earth can provide useful information about how mass is distributed around the planet and how it varies over time.

Most objects do experience some resistance from moving through the air. For low velocities, this drag force can be approximated as F=-bv where b is a constant that depends on the object’s shape and the properties of the air. This means that the acceleration will not be constant, and will instead have the form a_y=-g+\frac{b}{m}v, where v is a function of time, making this a differential equation and thus difficult to solve without special methods, although the change in acceleration can be observed if b is large enough.

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