DATA TABLES: TABLE I: + Mass of cart 0.5 kg Rubber Trial one Trial two Trial three Average bands Vf(m/s) vi (m/s) Vf(m/s) Vi (m/s) Vf (m/s) vi (m/s) Vf(m/s) vi (m/s) 0.582 -0.614 0.554 -0.569 0.570 -0.574 0.569 -0.586 2 0.968 -1.054 0.877 -0.841 0.942 -0.958 0.929 -0.951 3 0.780 -0.789 0.790 -0.796 0.745 -0.779 0.772 -0.788 4 1.101 -1.106 1.036 -0.961 1.001 -1.027 1.046 -1.031 5 1.213 -1.234 1.212 -1.221 1.262 -1.284 1.229 -1.246 6 1.576 -1.652 1.460 -1.527 1.599 -1.671 1.545 -1.617 TABLE II Rubber Impulse (Ns) Average bands Trial One Trial Two Trial Three (Ns) 0.670 0.632 0.638 0.647 2 1.09 0.955 1.04 1.028 3 0.721 0.735 0.696 0.717 4 1.071 0.967 0.988 1.001 5 1.322 1.338 1.381 1.347 5 1.732 1.642 1.759 1.711Averages TABLE III: Impulse (Ns) AV (rn/s) 0.647 1.155 1.028 1.880 0.717 1.560 1.001 2.077 1.347 2.475 1.711 3.162 ANALYSIS 1. Create an additional table (Table III) of Impulse vs. change in velocity. 2. From Table I, determine the average change in velocity and recorded in Table III. 3. Determine the average impulse for each trial and record these values in your data Table III. IMpulse vs. cahnge in velocity 1.5 O x Linear Fit for: Data Set | Average Impulse I = mx+b m (Slope): 0.558 Ns 1 - b (Y-Intercept): -0.0688 Ns Correlation: 0.985 Average Impulse (Ns) : 0.0773 Ns 0.5 - (1.093, 1.369) AV (m/'s) 4. Use Logger Pro and graph the data in Table III, Average Impulse on the y-axis and change in velocity on the x-axis. 5. Obtain the mathematical regression for the relationship between impulse and change in velocity: 6. Interpret the mathematical meaning of the slope and y-intercepts. What are the units of the slope express in basic units? -Math meaning of the slope: as the change in velocity increases 1m/s, the impulse increases 0.558 Ns/m/s, and the y-intercept indicates that when the change in velocity is ZERO, the impulse is -0.0688 Ns. 7. Determine the mass of the car. 8. Determine the percentage error for your lab: Ireal - calculated error X 100% real9. For any two trial determine the average force acting on the cart. To do this, you will need, the real mass of the cart, the initial and final velocities, the time interval of the charge in velocity. Favel m(vf-vi)_ [m(0.5823)-(-0.614m)] [m(0.582"3) +(0.614m) ] m(1.196m ) At Time interval from graph Time interval from graph Time interval from graph Favez m (v f - vi ) [m(0.5543)-(-0.5695)] _[m(0.554")+(0.5695)] m (1.123m ) ] At Time interval from graph Time interval from graph Time interval from graph 10. For the same two trial as in part 8, calculate the average force using the Impulse. Fave1 = - - = [0.670 Ns] At Time interval from graph Fave? = I [0.632 Ns] At Time interval from graph 11. Compare the forces for the two trial.CONCLUSIONS: I. Definitions -Linear Momentum: product of its mass and its velocity. - Impulse: an object's momentum changing when force is introduced for a period of time. - Momentum-Impulse Theorem: the impulse applied to an object will be equal to the change in his momentum. II. Physical Meaning of the slope and y-intercept III. General equations and its derivation: Linear Momentum: P = mv Impulse: J = F . At Change in momentum: Momentum-Impulse TheoremExplanation for possible errors. a. Calibration of the sensor is a possible error. IV. Textbook Correlation. - Chapter 7: Linear Momentum, section 7-1 Momentum fromhelium and Its Relation to Force