06/27/181Physics 211 Experiment #9 Impulse Momentum ExperimentDiscussionImpulse, momentum, and the impulse-momentum relationship are defined and discussed in the text. The momentum of an object with mass m and velocity is v.pmvThe impulse of a resultant force from time t1 to time t2 is When the force is plotted versus time, the impulse is the area under the curve between t1 and t2.21tres tF dtThe impulse-momentum relationship states that if an object with mass m is acted on by a force over the time interval from t1 to t2, the impulse is equal to the change in momentum:.2121tres tF dtppp This can easily be derived from Newtons second law .resdvFmamdtMultiplying both sides of the equation by dt we obtain, .resF dtmdvd mvdpIntegrating from time t1 to time t2, .221121tpres tpF dtdpppp In this experiment, a moving cart collides with a stationary “force sensor.” The force sensor measures the collision force as it varies with time throughout the collision. A motion sensor detects the position of the cart versus time, enabling its velocity to be calculated as a function of time. The computer graphs force versus time, and also the carts velocity versus time.A statistics package is used to integrate the force versus time curve to obtain the impulse. In addition, the initial and final (maximum and minimum) velocities can be obtained, making it easy to calculate initial and final momentum, and test the impulse-momentum relation.06/27/182Pre-Lab AssignmentComplete the following problem, using the impulse-momentum relationship. A 4kg mass is initially moving in the x direction at 5 m/s. A force in the positive x direction acts on the mass for 7 seconds as follows: a. The force grows linearly from 0 to 8 Newtons in 2 seconds. b. The force stays constant at 8 Newtons for 3 seconds. c. The force decreases linearly to 0 in 2 seconds.1. Calculate the initial momentum.2. Calculate the total impulse.3. Calculate the final momentum.4. Calculate the final velocity.(Hint: For parts 1 to 4 above, graph the force vs. time.)5. Answer the following question. A 4 kg ball moving at 3 m/s bounces off a wall and is observed to be moving at 3 m/s in the opposite direction. What was the total impulse on the ball?ApparatusPasco 750 Interface 1.2 meter dynamics track Force sensor attached to the Force sensor bracket with attachments (hook, rigid spring, less rigid spring, rubber bumper, magnetic bumper) Dynamic cart (without plunger) and mass block Motion sensor (set on “narrow beam) Pulley and clamp Large table clamp Mass holder and 500 grams of masses Thread Mass block to elevate trackDetailed Procedure and Analysis for the Impulse Momentum ExperimentI. Program Selection and Preparation Turn on the Pasco Science Workshop Interface, then the computer, and login.Launch the Data Studio program, choose Create Experiment, select Force Sensor, and Motion Sensor.Connect the Force Sensor lead to Channel A on the Science Workshop Interface box. Double click on the Force Sensor. In the Sensor Properties window, choose General, then select Fast Force Changes, and increase the sample rate to 1000 Hz. Under Measurement, de-select all choices and select Force (only Force should be checked). Click OK.Connect the yellow motion sensor plug into digital channel 1, and the other plug into channel 2. Double click on the Motion Sensor. In the Sensor Properties window, choose Measurement, then de- select Position and Acceleration, so only Velocity is selected. Choose Motion Sensor,and set the trigger rate to 100. Click OK.06/27/183To set up the graphs, drag the Force Sensor from the Data window to the Graph in the Displays window. Click and drag the Motion Sensor from the Data Window to the graph set up in the previous step. Two graphs should appear in the same window.To align the time origins of the graphs, click on the button at the top of the graph window with the Lock on it. II.Set-up of Track, Force Sensor, and Motion SensorFigure 1a. Arrangement of apparatus to calibrate the force sensor. A string is tied to a hook attached to the force sensorFig 1b. A close up of the clamp and pulley arrangement used to calibrate the force sensor.Figure 1c. The apparatus arranged to study a collision. The dynamics cart is rolling to the left. It will collide with a spring attached to the force sensor. (The spring is not visible in the picture.)Figure 1d. Close up photograph showing how the motion sensor clips to the end of the track.1.Set up the 1.2 meter track as shown in Figure 1a. Note that the left end of the track in Figure 1a is near the computer. The end of the track closest to the interface should be raised about 2 centimeters by using the black rectangular mass block, and should be at one edge of the table. The adjustable foot on the opposite end needs to be raised until it doesnt touch the table. The track needs to be braced, so that it wont move during a