Date Course Name Instructor Name Student(s) Name
Galileo Experiment An Energy
1. When Galileo introduced the concept of uniform acceleration, he defined it as equal increases in speed in equal intervals of time. This experiment is similar to the one discussed by Galileo in his book, Dialogues Concerning Two New Sciences, in which he assumed that a ball rolling down an incline accelerates uniformly. Rather than using a water clock to measure time, as Galileo did, you will use a Motion Detector connected to a computer. This makes it possible to very accurately measure the motion of a ball rolling down an incline. From these measurements, you should be able to decide for yourself whether Galileo’s assumption was valid or not.
1. Galileo further argued in his book that balls of different sizes and weights would accelerate at the same rate down a given incline or when in free fall. This was contrary to the commonly held belief of the time that heavier objects fall at a greater rate than lighter objects.
2. Since speed was difficult for Galileo to measure, he used two quantities that were easier to measure: total distance traveled and elapsed time. However, using a Motion Detector it is possible to measure much smaller increments of time, and therefore calculate the speed at many points down the incline. The data you will be able to gather in one roll of a ball down an incline, is more than Galileo was able to acquire in many trials. STUDENT OUTCOMES
Through this experiment, students will be able to: - Use a Motion Detector to measure the speed of a cart down an incline. - Determine if Galileo’s assumption of uniform acceleration is valid. - Analyze the kinematic graphs for a cart on an incline. - Use Energy conservation to predict the maximum velocity of the cart.
MATERIALS
Tablet PC Computer Laptop Vernier computer interface Logger Pro Vernier motion detector Inclined plane 1-3m cart
PRELIMINARY QUESTIONS
1. If you were going to drop a small mass and a large mass from the same height at the same time, would you expect the larger one to hit the ground first, last, or at the same time?
2. Now do it: drop a small mass and a large mass from the same height at the same time (please do this outside or you might just make a hole in the ground ;). Did the larger one hit first, last, or at the same time?
3. State clearly what Galileo claimed concerning the outcome of this simple experiment.
4. Is your observation consistent with Galileo?
PROCEDURE
1. Place the motion detector at one end of the wooden board as shown in the picture, and place the cart 0.2 m away from it. Place masking tape in front of the cart. Insert several masses under the board where the motion detector is and measure carefully the height between the table, where the board lies, and the position of the masking tape where the cart will be released from (a height of roughly 10 cm is suggested). 2. Open the file “03 Modern Galileo” from the Physics with Computers folder. 3. Click to begin data collection. Release the cart when you hear the Motion Detector start to click and catch it when the front is exactly at the edge of the other side of the board. 4. From your graph, measure the value of the velocity as the cart reached its lowest position. 5. Repeat the procedure by adding more masses (20 grams at a time) on the cart and record your values. Please include the maximum height (where the masking tape is) and minimum height (other side of the board where you caught the cart). Be very careful to do all trials from the same starting and ending points! You are free to measure your height from any point of your choice (hint hint!! but if this statement is confusing to you, simply disregard it :).
Mass (kg) Velocity (m/s)
Minimal height:______m Maximum height:______m 6. Include the Vernier graph for the highest mass trial.
ANALYSIS
7. Plot a graph of velocity vs mass with excel. Pay special care to your y scale! (remember the pendulum experiment!) and insert the best fit line. 8. Based on your graph, what can you conclude about the effect of mass on the final velocity (and therefore on the motion of the cart)? Use the value of your slope to justify your statement. 9. Do your experimental results confirm what Galileo said 2000 years ago? 10.You are now expert in applying energy conservation to deduce the final velocity of the cart. So first, write down the energy conservation law. 11.Write down the total energy right before the cart is released. 12.Write down the total energy right before the cart was caught. 13. Use the energy conservation law to deduce the final velocity of the cart using data from the highest mass amount. Of course, you are not to use the velocity obtained by measurement (table values) in your calculations. The point is to derive the velocity using energy conservation arguments, and compare it to the experimental value from your table (we are doing the exact same thing as the previous experiment here). 14. Compute the percent error, and make a statement on the accuracy of your result.