Hang Time Activity Background: Gravity is everywhere! Without it, you would float away by just walking. If you were sleeping on your belly at night and sneezed, you would float to the ceiling. (That would be pretty cool actually.) Drinking juice in the morning would mean catching little orange spheres of fluid in midair. There is even a gravitational attraction between you and your pet. If an object has mass, then there is a gravitational attraction between the object and the surrounding environment. In this lab you will investigate how objects fall under the influence of gravity. By simply jumping underneath a computer-driven motion sensor, you can measure your distance, velocity, and acceleration for an entire jump. The sensor uses high frequency sound waves to measure your distance away from it many times per second. The results are then displayed on a graph and in a table on the computer. Believe it or not, the acceleration you experience while in the air is identical to that experienced by Michael Jordan when he dunks a basketball. Although I doubt your vertical jump and hang time are identical! www.ocf.berkeley.edu/ ~ericfeng/michael_jordan.htm Objectives: 1. Measure each group member s vertical jump height and hang time. 2. Analyze how a jumper s motion changes during a vertical jump (1 dimension) through motion graph analysis. 3. Apply a quadratic equation of motion to a distance vs. time graph to determine the magnitude (size) and direction of the acceleration for a falling object near the Earth. 4. Investigate the effect of one variable on a jumper s acceleration while in the air. 5. Compare your group s results for g, the acceleration of free-fall, to the class average. The average should fall within 5% of the accepted value of 9.8 m/s 2. Purpose: To find the acceleration of an object in free fall and its dependency on variables. List 4 factors that you think might affect the rate at which an object falls under gravity only. 1. 2. 3. 4.
Materials: Computer with Logger Pro/Data Studio software Lab Pro/Science Workshop 750 interface Motion Detector Link Cable Printer Jumper You also might be able to use an Explorer GLX from Pasco with Data Studio. Procedure: 1. Listen to all verbal directions because they are also important. 2. Have one student stand directly beneath the detector standing straight up and still, arms at his or her side. 3. Click start on the graph - you should hear the detector start clicking. 4. Have the student bend, jump straight up, and land again, returning to a standing position. Keep the head very still and facing forward. 5. Click Stop on the graph to stop the detector once the graph becomes flat. 6. You should now have a graph of distance vs. time like shown below. If it isn t smooth, try again! 7. Print the actual graph and attach it on the next page. Yes, each person needs a copy. Can you figure out what the little tails represent? (Think about the entire motion of the person, including bending the knees to jump and landing.) 8. Describe in words, every portion of the motion by circling at least 12 unique sections of the motion on the graph and labeling them with a number and description.
9. Sketch the corresponding vt and at graphs for the jump below. DO NOT use the data studio program to make these-they aren t right. Circle the corresponding sections (1-12) that correspond to your dt graph. For example, if the slope of your dt graph is 0 at any point, then at the same time on a vt graph your line should pass through the t axis. I want to see both graphs match up perfectly without any doubt that you fully understood all 12 sections of each graph. 10. Using the dt graph you printed, determine the vertical jump height and hang time for each jumper. The cursor or trace function should help you find the proper coordinates here.
Again, use the cursor or trace function on the program to find the values. 11. Follow your teacher s printed instructions to create a best-fit line for your parabola data pasted in Excel that corresponds to the time while in the air only. 12. Copy down the equation of best fit (polynomial, degree 2) for the free-fall portion of the jump: y= x 2 + x+, r 2 = 1-RMSE= A B C Value of A: Accepted Acceleration due to Gravity, g =: Value of B: Your Experimental Value of g from the graph: Percent Error from Accepted Value: % Value of C: % Error = experimental value accepted value x100 accepted value 13. Save the data file and graph, then print out 1 copy of the graph per group. Experimenting and Applying: Now that your group has some ideas about things that can affect jumping motion, develop a lab investigation examining the relation between two variables for a jump. Design a researchable question below with your group. Researchable Question (How does X affect Y?): Hypothesis (X will affect Y in this way because...): Independent Variable (What you vary directly):
Dependent Variable (What you are measuring as result of the lab): Controlled Variables (What do you need to make sure doesn t change each time?): 1. 2. 3. Complete the following on this sheet only, attaching any necessary graphs. Data: Print out graphs that prove how X affects Y. Analysis: What do the graphs mean? / Any calculations needed to prove your point. Conclusion: Use the physics lab write-up guidelines and Documenting a Scientific Investigation to help you. This must be preliminarily hand written as a group on the back of this page.