Impulse Momentum Experiment

Transcription

1 Impulse Momentum Experiment Discussion Impulse momentum and the impulse-momentum relationship is defined and discussed in the text The momentum of an object with mass m and velocity v is p = mv The impulse of a resultant force from time t 1 to time t 2 can be represented graphically When the force is plotted versus time the impulse is the area under the curve between t 1 and t 2 t2 F resdt t1 The impulse-momentum relationship states that if an object with mass m is acted on by a force over the time interval from t 1 to t 2 the impulse is equal to the change in momentum: t2 F resdt = Δ p= p2 p1 t1 This can easily be derived from Newton s second law dv Fres = ma = m dt Multiplying both sides of the equation by dt we obtain F dt = mdv = d mv = dp res ( ) Integrating from time t 1 to time t 2 t2 p 2 F dt = dp = p p =Δp res t1 p1 2 1 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 cart s 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 01/11/09 1

2 Pre-Lab Assignment Complete 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? Apparatus Pasco 750 Interface 12 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 track Detailed Procedure and Analysis for the Impulse Momentum Experiment I Program Selection and Preparation Launch the Data Studio program choose Create Experiment select Force Sensor and Motion Sensor 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 Measurements window de-select Position and Acceleration so only Velocity is selected Set the sample rate to 100 To set up the graphs drag the Force Sensor from the Data window to the Graph in the Displays window Connect the Force Sensor lead to Channel A on the Science Workshop Interface box Increase the sample rate to 1000 Hz Under Measurement check that force Force is checked 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 01/11/09 2

3 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 Sensor Figure 1a Arrangement of apparatus to calibrate the force sensor A string is tied to a hook attached to the force sensor Fig 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 12 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 doesn t touch the table The track needs to be braced so that it won t move during a collision Place a large table clamp approx 15 m from the computer and brace the far end of the track against this clamp 2 Attach the force sensor bracket with the force sensor attached near the low (far) end of the track 3 Attach a universal clamp and pulley to the opposite end of the track Adjust the position of the track so the pulley and clamp are over the edge of the lab table This pulley assembly will be used with 500 g of mass to calibrate the force sensor 01/11/09 3

4 4 Measure the vertical height of the track at the rectangular block (measure the distance from the table top to the bottom of the track) and also measure the distance along the track from the block to where it touches the table Use an appropriate trig function to calculate the angle of the track 5 Weigh the dynamics cart and record its mass in kilograms III Calibration of Force Sensor The force sensor must be calibrated at the beginning of this experiment If these instructions are not followed EXACTLY you might get a negative force instead of a positive one when the apparatus is used to measure the force 1 Click on the Calibrate Sensors Tab that appears along the top of the Experiment Setup window 2 With no force pulling on the force sensor push the Tare button on the side of the force sensor Find Calibration Point 1 on the computer screen Change the -50 Newton value to zero and click on Read from Sensor 3 Set up a pulley at the high end of the track so that a string from the force sensor hook can pass over the pulley to a hanging 500 gram mass Do not press the Tare Button again at this point! 4 Attach a total of mass of 500 grams to the string so that the force applied to the force sensor is (5kg) (98 m/s 2 ) = 49 Newtons 5 Find Calibration Point 2 and change the 50 Newton value to 49 and click on Read from Sensor 6 To check the calibration look at the Present Sensor Measurement When the string exerts no force the Present Sensor Measurement should display 000 Newton ( + about 03N) When the 500 gram load is applied the Present Sensor Measurement should display 49N ( + about 03N) Check to insure that these readings are accurate 7 Click on OK IV Set Up the Motion Sensor and Record Data from a Collision 1 Replace the pulley and clamp with the motion sensor Clip the motion sensor onto the track at the high end of the track 2 Set the switch on the motion sensor to Narrow Beam Aim the motion sensor slightly downward toward the track 3 Remove the hook from the force sensor and replace it with the bumper holding the more flexible spring 4 Place the dynamics cart (including the mass block) on the track at least 40 centimeters from the motion sensor 5 Push on the tare button on the force sensor to zero it 6 Click on Start 7 Release the cart 8 After the cart bounces off the force sensor and rolls uphill click on Stop 9 If the velocity data has large spikes in it call the instructor over to check your results NOTE: Be careful not to get into the ultrasonic beam emanating from the motion sensor or it will detect your movement not the movement of the cart! V Obtaining Results from the Graphs From the graph of force versus time you will need to determine the impulse and from the graph of velocity versus time you will need to determine the change in momentum (see page 1 of this writeup) 01/11/09 4

5 In addition as described below there is a small correction to the measured impulse due to the force of gravity on the cart during the collision; to make this correction you will need to know the collision time interval 1 Click on the Zoom Select button 2 Drag a zoom rectangle enclosing the collision region of the force versus time graph and include only a small amount of data before and after the collision 3 The impulse is given by the area under the curve on the Force versus time graph To obtain this click on the Legend Box within the Force versus time graph so it becomes yellow Select the down arrow next to Σ (which represents statistics) De-select everything that is checked and select Area The area under the curve will appear on the graph Record this value 4 To obtain the maximum and minimum velocity select the Legend Box within the velocity versus time graph so it becomes yellow Select the down arrow next to Σ (statistics) De-select everything that is checked and re-select maximum and minimum The maximum and minimum values of the velocity will appear on the graph Record these values 5 From the graph record the time of the beginning and end of the collision by using the Smart Tool found at the top of the graph window (it looks like coordinate axes) Double click on the graph window and select Graph Settings Set the Data Point Gravity to 0 VI Obtain Additional Data Make a second run by repeating the steps outline above In addition make two runs using each of the other three bumpers: the more rigid spring the rubber bumper and the magnetic bumper Remember to push the tare button before each run Print out one graph for each bumper For the magnetic bumper the collision is more extended in time The zoom rectangle must include all data points from the full duration of the collision VII Calculations For each run calculate the initial and final momentum of the cart using the initial and final (maximum and minimum) velocities of the cart and calculate the change of the momentum of the cart Compare the change in momentum with the impulse of the resultant force and calculate the percent difference (See the following note for the correct method to calculate the impulse Note: Follow the instructions below unless instructed otherwise Theoretically the change of the cart s momentum should equal the impulse of the resultant force on the cart The resultant force equals the bumper force minus the downplane component of the cart s weight But the force sensor can only measure the impulse of the bumper force So a correction must be made to find the impulse of the resultant force (Since the correction is small your instructor may tell you not to make this correction) To make the correction calculate Fxg = mgsinθ the down plane component of the cart s weight Calculate the total collision time Δ t = tf ti Δ t = t f - t i Calculate Fxg Δ t Subtract Fxg Δt from the recorded impulse of the bumper force to obtain the impulse of the resultant force 01/11/09 5