Lab5

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Rutgers University *

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Civil Engineering

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Oct 30, 2023

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Collision I Lab Report Names:Ting Cheung Tung Section:H5 Date:Oct 29 Purpose To investigate the relationship of impulse to change of momentum Readings You can explore the Wikipedia or your favorite mechanics textbook, Elastic collision, Inelastic collision, Kinematics, kinematics equations, Impulse Theory and concepts in short In a collision it is difficult to use Newton’s Second Law, F = m a because the force varies with time in some generally unknown manner. (Note: a bold letter for F means it is a vector unlike mass, m, which is a scalar.) We can rewrite the second law in a manner more useful for collisions by using the impulse I = ∫ F dt. Integrating both sides of the second law, I = ∫ F dt= ∫ m a dt = ∫ m d v dt dt = ∫ m d v = m v f - m v i where v f and v i are the velocities of m before and after the collision. Notice that F in here is the total force acting on the body. We define the linear momentum of m as P = m v . Then the second law says that the change of momentum of a body during a collision equals the impulse it receives, I = Δ P. Procedure Procedure for Part I When a dropped ball hits something it exerts a force on it (and by Newton’s third law an equal force is exerted on it). We will use the force probe to measure that force. You will drop a play-doh ball and golf ball with the same mass from the same height. The golf ball undergoes a nearly elastic collision while the clay ball has an inelastic collision. Setting Up the Data Collection Program LoggerPro Tung_Lab5_Collision1.nb 1 Printed by Wolfram Mathematica Student Edition

- Load the computer program LoggerPro by double clicking on its icon. - Add the force detector which is facing upward by clicking on the LoggerPro icon , and then clicking on the CH1 ⇒ Choose Sensor ⇒ Force ⇒ Dual Range Force - Gently press on the force probe. You should see a live reading at the bottom-left of the screen that shows the force you are exerting in units of Newtons. - Make sure that the button on the back of force probe is set to ± 50N . Make sure this is also the case on the settings of the sensor in the LoggerPro. If not use Change Sensor Range option to change it to ± 50N . - Zero the force probe by clicking zero icon. (Do this before each measurement, also after the measurement check to see if it is still close to zero and not drifted too much by the bounces.) - Click on the clock icon. Set the data collection rate to 4000 Hz for 0.5s . Tung_Lab5_Collision1.nb 2 Printed by Wolfram Mathematica Student Edition

and trigger level of 1N , and 100 Samples before Trigger data. When you press Collect, LoggerPro will wait until the probe reads a force of at least 1 N (this is called “trigger- ing”), and then collect data. To check that this is working, press the Collect button. No data should be collected. Drop the golf ball through the plastic tube so that it hits the force probe. A plot of Force vs Time should now appear, showing at least two significant peaks. If the triggering does not happen, check and see if the force probe is measuring negative values when you press on it. If this is the case, reverse the reading of the force sensor by clicking on the sensor icon and check-marking Reverse Direction . Procedure for Part II In the second part we will make a similar measurement with a rolling cart hitting the force probe.The velocity will be measured using the motion detector.The motion detector cannot take data at the high rate we need for the force detector, so you will have to use an independent motion detector (i.e., not the one Tung_Lab5_Collision1.nb 3 Printed by Wolfram Mathematica Student Edition

connected to the same ULI as the force probe). Setting Up the Data Collection Program LoggerPro For this part, you will work together with another lab group. One group measures the force excerpted by the rolling car, the other group measures the velocity of the cart before and after collision using a motion detector. - Add the motion detector by clicking on the LoggerPro icon and then clicking on Dig/SONIC1 ⇒ Choose Sensor ⇒ Motion Detector - Click on the clock icon, and set the data collection rate to 50 Hz . Dialog: Part I. A Golf Ball, A Play-doh Ball, & The Force Sensor Tung_Lab5_Collision1.nb 4 Printed by Wolfram Mathematica Student Edition

When a dropped ball hits something it exerts a force on it (and by Newton’s third law an equal force is exerted on it). We will use the force probe to measure that force. You will drop a play-doh ball and a golf ball with the same mass from the same height . The golf ball undergoes a nearly elastic collision while the clay ball has an inelastic collision. Which do you expect to exert the greater force? Golf ball The contact time of the golf ball is shorter, so I guess it will exert a greater force. Step 1. Measuring the Impulse delivered to golf ball by the force probe - Zero the force probe. Press Collect and drop the golf ball through the plastic tube so that it hits the force probe. - Export your data into a CVS file and then import it into Mathematica using the Import function. (g1 is to label “golf ball’s 1st trial”) Example: fvtg1=Rest[Import[“/home/maryam/Downloads/f1.csv”]] - Now you can plot your force vs time plot using ListPlot function. Example: ListPlot[fvtg1, Joined  True, PlotRange  All, Frame  True, FrameLabel  {“Time (s)”,”Force (N)”}] 0.00 0.05 0.10 0.15 0.20 0.25 0 5 10 15 20 25 Time ( s ) Force ( N ) - From the plot find t0 (* time at which golf ball first hits probe (beginning of the first bounce) *), t1 (* time at which golf ball leaves probe (end of the first bounce) *), t2 (* time at which golf ball hits probe for the second time (beginning of the second bounce) *) and record below. - Measure m using the scale. - Measure h using a ruler. (You may find it convenient to measure the length of the plastic tube and the height of the force probe hook.) Tung_Lab5_Collision1.nb 5 Printed by Wolfram Mathematica Student Edition

In[5]:= fvtg1 = Rest [ Import [ "C:\\Users\\User\\Desktop\\Mathematica\\Tung _ Lab5 _ Collision1\\g1.csv" ]] ; ListPlot [ fvtg1, Joined  True, PlotRange  All, Frame  True, FrameLabel  { "Time ( s ) ", "Force ( N ) " }] fvtg2 = Rest [ Import [ "C:\\Users\\User\\Desktop\\Mathematica\\Tung _ Lab5 _ Collision1\\g2.csv" ]] ; ListPlot [ fvtg2, Joined  True, PlotRange  All, Frame  True, FrameLabel  { "Time ( s ) ", "Force ( N ) " }] fvtg3 = Rest [ Import [ "C:\\Users\\User\\Desktop\\Mathematica\\Tung _ Lab5 _ Collision1\\g3.csv" ]] ; ListPlot [ fvtg3, Joined  True, PlotRange  All, Frame  True, FrameLabel  { "Time ( s ) ", "Force ( N ) " }] Out[6]= 0.0 0.1 0.2 0.3 0.4 0 2 4 6 8 Time ( s ) Force ( N ) Out[8]= 0.0 0.1 0.2 0.3 0.4 0 5 10 15 Time ( s ) Force ( N ) Out[10]= 0.0 0.1 0.2 0.3 0.4 0 5 10 15 Time ( s ) Force ( N ) Tung_Lab5_Collision1.nb 6 Printed by Wolfram Mathematica Student Edition

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