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  LPC Physics Jumping Force Force , Mass, and Motion Introduction: In this lab you use logger Pro and the Force Plate sensors to help you determine the difference between Mass and Weight, as well as understand the relationship between the height of a jump and the force exerted on the force plate. Equipment:      Logger Pro    Force Plate    Meter stick    Chalk Image from: www.umbc.edu/happ/health/IFR.htm   Theory:  The acceleration of any system is equal to the net external force, divided by the total mass of the system, as given by Newton’s Second Law of Motion. In other words: net total F a M  =  In a coordinate system that points upwards from the ground, we can identify the forces and assign signs (+ or -). Imagine that you are standing on a scale, so that there are now two forces acting on you. The downward force of gravity (mg) and the upward force of the scale on your feet (F n ) ( ) nn net total F mgamF m a g F a M  −== + =  In this case, F n  is the force of contact between you and the scale. This is often called your “apparent weight ” Note that If you are in the air and not touching anything, , then F  n  = 0, and 0 = m(a+g), so a = -g. h 1 of 5  LPC Physics Jumping Force In this lab, our goal will be to verify Newton’s second and third law, and understand how  Newon’s laws work together with the kinematic equations you learned eaerlier in the class when you jump in the air. In a nutshell, you will jump off the scale and see how high you get. From this height, and a measurement of how much your body moved  before you left the scale, your acceleration while in contact with the scale  can be calculated. From this value, and knowledge of your weight, we can predict how much force you must exert on the scale while you are jumping. This can be compared to the actual value measured on the scale and Newton’s laws can be verified. So lets get started! A)   Determining your acceration while in contact with the scale. To determine your acceleration, you will need to know both the speed you left the ground, how much you bent your knees and how high you jumped To do this, we will use the relationship below twice: Equation (I) 2 20 2 ( ) o v v a y y = + −   To find a, use the following conventions: 1)   at the top of your jump, v = 0, and your speed at the start of the jump = v 1 . 2)   while you are in the air, a = -g 3)   While your feet are in contact with the ground, your speed at the start of the jump = 0, and your speed as you leave the scale is v 1 . While you are in contact with the scale, the average acceleration = a. 4)   The distance your center of gravity moves while you are in contact with the scale = d So: While you are in contact with the scale, Equation ( Ia) 2 21  0 2 ( ) v a d  = +   And While you are in the air: Equation ( Ib) 221 02() vgh = −  Thus equations Ia) and Ib) can be combined to find a, the acceration you have while you are in contact with the scale. The predicted value of F n  is then: II) () n Fmag = + = ma + mg Where: mg = your weight in Newtons while standing at rest on the scale. m = your weight divided by g (9.80 m/s 2 ), and a is the acceleration from equations (Ia) and (Ib) above. The experimental value of F n is the reading on the scale while you are in contact with it. Of course this will vary, so the trick is deciding which value of F n to use! 2 of 5  LPC Physics Jumping Force Procedure:  1.   Connect the Force plate and logger Pro to the computer. Make sure the collect button is working and the display reads Force as a Function of time. Press on the Force plate and see if the reading changes. 2.   Check the Calibration of the Force plate by placing weights on the force plate.You may have your best results by doing a “one point calibration” twice. If there is difference between the two, you will need to calibrate the program. Your instructor will show you how if you are having difficulties. Fill out the Mass Calibration Table and show sample calculations. It should not be difficult! 3.   Each of the lab partners should take turns standing on the plate. Fill out the “Force and Weight” table  and show your calculations. 4.   While standing on the force plate, practice using a two meter stick to measure the distance one lab partner bends his or her knees when jumping (the height of your center of mass will change when you bend your knees), and the height of the jump. 5.    Now the same person should jump in the air and touch a spot on the wall or two meter stick so the height of the jump can be measured. You should record the distance his or her knees are bent, and the height of jump for the same jump! 6.   During the jump, collect data on Force vs. time. For the value of the force, find the  peak force during the jump, and a time average. To get a time average, highlight the Force vs time graph, and integrate over the time interval while jumping. Then divide the result by the time interval. your weight, and average them together: Repeat for each lab partner and fill out the “Jumping Data” table. Also Make a Sketch of the display of your Force vs. time graph. Save your graphs for part 8  below. 7.   Use the Expected vs. Measured force table to help you determine the results of your experiment. 8.   Can you think of a better way (analyzing the logger pro data) to determine the average force while you were jumping (F n )? If so, do it. You can use the predicted value of the force to help you decide which method works best! 9.   Think of one other investigation you can do using the force table and do it! 10.   When you are done, you can turn in the lab tables and calculations below as well as ONE additional page with your introduction, a sketch of one Force vs. time graph, A sketch of a person in the act of jumping with forces drawn in, a description of what you did in #9, and a one or two additional sentence summary of results. 3 of 5  LPC Physics Jumping Force  Names of Lab Partners: Mass Calibration Table mass expected reading in  Newtons actual reading in Newtons  before calibration 1 kg 2 kg Calculations: Table 1: Force and Weight  Name Weight in  Newtons Mass in kg Weight in lbs Calculations: Table 2: Jumping Data  Name Distance knees are  bent Height of jump Max Force during Jump Time average Force during Jump Trial 1 Trial 2 Trial 3 Calculations: Show one sample of each calculation! Sketch of Force vs. Time graph (use straight edge and include units!) 4 of 5
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