Names:
Freefall Motion
Equipment
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Clamp, 90º
Meter Stick (2)
Smart Timer
Ring Stand, 120 cm
Steel Ball (w/ apparatus)
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Typical Setup
Introduction
An object dropped near the Earth’s surface will fall with an acceleration of g(the acceleration due to gravity, 9.80 m/s2), independent of its mass. This was the famous observation of Galileo. This is true specifically when air friction effects are negligible. Thus in a vacuum, a feather falls as quickly as a gold ring. The kinematic equation (an equation which determines the position of something at any time) which describes the vertical position of an object at any time if it is dropped from rest is
.
The value of g will be determined experimentally and compared to 9.80 m/s2.
Procedure
- Set up the ball release mechanism on a vertical stand that will allow various heights y to be arranged for the mechanism.
- Place the steel ball in the mechanism and set the tightening screw so that the ball is secure.
- Place the stop timer directly underneath the ball.
- Measure the height y as shown in Figure 1.
- Reset the timer. Release the ball. Record y and t for the fall.
- Repeat at different heights for a total of five data points.
Data
Trial Number / Height, y(meters) / Time, t
(seconds) /
(seconds squared)
1
2
3
4
5
Analysis
The general formulation for a straight line is
,
where
m = the slope and b = the y-intercept.
If we compare this equation to our kinematic equation we can relate the two by defining
Then if we make a graph of height, y, versus on the x-axis, the slope of the resulting line will be g. Using Microsoft Excel® make a graph of your measured values of height (y-axis) versus one-half elapsed time squared (x-axis). Include a best-fit line and its equation with the slope.
Questions
- Interpret the results of your graph. What is your value for g? ______
Show your equation of best fit line and relate it to the expected results.
2. What is the percent difference of your value from 9.80 m/s2?
% difference =
3. Is your value of g reasonable? Explain why or why not. What are some possible sources of experimental error? Be specific about what errors could have been present.
4. Measure reaction time of at least two members of your lab group. One person should hold a meter stick from one end, hanging vertically. A different person will hold their fingers on opposite sides of the meter stick at about the 50 cm mark. Without warning the first person will drop the meter stick and the second person will try to catch it as quickly as possible. Measure the mark at which it is caught and determine the distance the stick dropped in that time. Do at least three trials per student and average the results for the distance.
Use the equation and make sure you are using the correct units. Substitute the value of g(9.80 m/s2), and the distance the stick dropped (y) to calculate the reaction time, t, of the students catching the stick.
Data Table
Student Name:Trial 1 Distance (m)
Trial 2 Distance (m)
Trial 3 Distance (m)
Average Distance (meters)
Reaction Time
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