Physics 2211, Sim 02: The Acceleration due to Gravity
Eric Murray, Summer 2020
Question this simulation will enable you to answer: What is the acceleration due to gravity in this simulation?
Features: The simulated object is on a ramp (a one-dimensional space) without friction.
Approach: One end of the ramp is raised to some suitable height. The position of the object at several times is measured as it moves down the ramp. The acceleration is calculated as the slope of a velocity vs. time graph.
Preliminaries: Open the Ramp: Forces and Motion simulation. Select the Force Graph
tab. Choose an object (the File Cabinet provides the longest run) and an ice (no friction) surface. Set the height of the ramp with the Ramp Angle control so the angle is approximately 5°. Display, on the graph, the component of the gravitational force parallel to the ramp. Move your object to the upper end of the ramp (the Object Position control is simplest).
Experiment 1: Play
(▶) the simulation. You may stop the simulation once your object exits the ramp.
Analysis: Expand the horizontal (time) scale of the force graph to 6 sec full-scale. Note that the component of the gravitational force parallel to the ramp becomes zero when the object exits the ramp. Playback
the recording of your experiment one step (❘▶) at a time. Determine how much time each step represents.
Record the position of the object for at least 10 positions spread over the motion down the ramp. Calculate the average velocity of the object between each pair of sequential time steps (that is, between t1 and t2, between t2 and t3, etc.), begining when the object first begins to move.
Graph the average velocity of the object as a function of time, using a spreadsheet such as Excel. Perform a regression analysis to find the slope of the graph and its standard error (a ± Δa). Calculate the acceleration due to gravity, g ± Δg.
Experiment 2: Repeat Experiment 1 with a Ramp Angle of approximately 10°.
Summary: Review your results. Compare them with your expectations from reality.