Name___________________________
H Physics
Galileo’s Diluted Gravity Lab (50 pts)
Note: this lab will be written on your own paper. The order of items in the lab report is to be:
Experimental Design, Procedure, Data, Graph, Mathematical Model, Analysis, Conclusion.
Objective
To determine the value of g, acceleration due to gravity, experimentally. First, you will graphically
determine the acceleration of a cart on a ramp of angle  and then calculate a value for g using the
relationship a  g sin  .
Background
In the 17th century, Galileo investigated gravity by rolling balls down ramps. If the clocks of his day had
been better, he might have investigated free fall directly but he had sand and water clocks, which meant
that short periods of time could not be measured accurately. In effect, his ramp diluted gravity, slowing
freefall down yet still retaining the essential mathematical relationship between time and distance.
Guidelines for the Procedure
Like Galileo, you will use a ramp to decrease the acceleration of the cart. Using the photogates, you will
determine the velocity of the cart at several different displacements distributed throughout the ramp.
You will also determine the time it takes to travel to each of those displacements. The experiment works
best when the ramp angle is less than 20 degrees. Be sure to record this angle. Come up with a
repeatable method for releasing your car just before the first photogate so that it has an initial velocity of
zero. Be sure to describe this method in your procedure.
Materials
Ramp, cart, photogate timers, meter stick.
Instructions
Design of Experiment (4 pts)
testable question
independent variable
dependent
variable(s)
2 controls
hypothesis
because
Procedure (5 pts). Describe your steps in your own words. It may be in numbered form or paragraph
form. Explain how you collected velocity data and how you collected time data.
Data (5 pts). In this lab, you will be collecting both final velocity and time data for several (5 to 6)
displacements. Make the displacements span the range of the ramp; make sure some are small and some
large.
Graph (6 pts). Instead of graphing dependent vs. independent variable, graph final velocity vs. time
(time is always on the x-axis). Draw the graph on your paper: give it a title and label the axes including
units. Draw a line of best fit (do not connect the points). Do a linear regression on a calculator to generate
an equation of the line. Insert your TIME in LIST 1 and your FINAL VELOCITY in LIST 2.
Mathematical Model (6 pts). A mathematical model is an equation of the line using the variables in
your graph instead of x and y. In your model (equation), include units on your independent variable,
dependent variable, and the slope.
Analysis
1. Analyze the mathematical model. (4 pts)
a. What is the value of the slope, including units?
b. What is the value of the y-intercept, including units?
c. What kinematic equation does this look like? What is the physical meaning of the y-intercept?
2. To complete this item, you will use the Video Physics app on an iPhone or iPad. (8 pts)
Film your cart going down the ramp. Then go frame by frame to mark the position of the wheel of the
cart. Also make the scale and tilt the axis so the x-axis is down the ramp. Then send the file to
yourself and to your teacher so you can keep the data and view the graphs.
a. Sketch the x vs. t graph from Video Physics. Label the axis and include units.
b. Sketch the v vs. t graph from Video Physics. Label the axis and include units.
c. Determine the slope of the v vs. t graph. Record with units. Compare to the slope from 1a using
% difference. Show work.
3. Like Galileo did, find an experimental value for g, acceleration due to gravity, using the expression
a = gsinq . (6 pts)
a. Re-arrange the equation for g. Then substitute and solve. The “a” value is the acceleration down
the slope, which you have obtained two ways.
b. Compare your experimental value for g to the theoretical value of g = 9.81 m/s2. Use the percent
error calculation to compare. Show your work.
Conclusion (6 pts)
Write a 4-5 sentence conclusion. State the findings of the lab. Specifically address:
 Findings from the v-t graph
 Findings from the x-t graph
 What you learned from the video capture
 The experimental value of g
 At least two sources of error that might have caused your value of g to differ. (Note: human error
is not a source of error. An example of a source of error is “It was difficult to determine the angle
because we did not have a protractor.”)
Bonus (4 pts): Find the equation of your x-t plot using a power fit or a quadratic fit. Write the equation
of your line/curve with the variables in your graph. Solve for the acceleration of your cart and compare it
to the acceleration from 1a and 2c.