IMPULSE AND MOMENTUM Exp. #16
(Alward/Harlow Web File: "impulse.doc" 3-3-04)
Name: ______Partner(s): ______Sec. Num: ______
Equipment:
2.2 meter track level Collision Cart Motion Sensor Force Sensor Masking Tape Force Sensor Bracket with Collision Bumper Pan Balance
Instructor: Force sensor should be set to "low sensitivity", (-50V, 50V) at (8V, -8V).
I. PURPOSE AND THEORY
In this activity the student will verify that the impulse delivered to an object equals the change in that object’s momentum.
In one dimension, the momentum of an object of mass m and velocity v is given by p = mv. The direction of the velocity is designated with a positive or negative sign. Thus, an object traveling to the right along the positive x-axis may have a velocity v = 12 m/s, for example. However, if the object is traveling along the negative x-axis, its velocity would be v = -12 m/s. Thus, an object moving in one dimension may have either positive or negative momentum.
Suppose an object is traveling to the right with momentum p0 = 48 kg m/s. Further suppose that it collides with some object and reverses its direction of motion; after collision, imagine that the momentum is p = -32 kg m/s. The change in the object’s momentum is therefore p - p0 = (-32-48)= -80 kg m/s. We say that this object has experienced an impulse of -80 kg m/s.
The impulse delivered to an object by some force F(t) during some time interval is the integral of F(t) with respect to time. The lower limit of integration is the beginning instant of time, and the upper limit is the final instant of time. Note that impulse may be calculated over any time interval, not necessarily the interval which covers the entire duration of the force application or the duration of the collision. Normally, one is interested in the impulse delivered during the entire period of time in which the force was acting on the object. The impulse-momentum equation is given in Equation 1.
mv - mv0 = area under force-time curve (1)
II. SETUP
If Science Workshop is already opened and the force and velocity graphs are on the screen, the user may skip Steps 1 and 2 below.
1. Turn on the Signal Interface, then turn on the computer.
2. Open the file “impulse.sws”.
Some of the steps below may already have been completed earlier.
3. Remove the hook from the force sensor and screw it into its storage space on the side of the Force Sensor Bracket; remove the magnetic bumper from the Force Sensor Bracket and attach it to the end of the force sensor.
4. Remove the two black plastic screws attached to the force sensor and attach the force sensor to the underside of the force bracket.
5. Using the two thumb screws and square nuts, slide the force bracket with force sensor onto the track at about 190 cm; put 200-cm end of the track up against the wall to absorb shock.
6. Attach the force sensor plug to Analog Channel A on the interface. Connect the motion sensor plugs to Digital Channels 1 and 2 of the interface; the yellow-banded cable goes into Channel 1 and the second plug into Digital Channel 2.
7. Place the motion sensor near the 80 cm mark on the track. This sensor will be used to measure the velocity of a moving cart during the period of time that it is colliding with the force sensor. Use masking tape to secure the sensor to the track.
8. Attach a 3x5 inch card to one end of the collision cart. This card will allow better reflectivity of the ultra-sound waves.
9. Zero the force sensor by pressing the TARE button on the side of the sensor.
III. PROCEDURE
1. Measure the mass of the cart with reflecting card. Record the mass in the table. Place the back end of the cart at the 90-cm mark. Level the track.
2. Give the cart a push toward the force sensor, then click on RECORD or press ALT-R. Avoid noisy, track-moving collisions with the bumper. Imbedded in the front of the cart are magnets which will be repelled by the magnetic bumper, so if the initial speed of the cart is not too great, a collision without contact will occur. Make sure the force sensor and bracket are very securely attached to the track, otherwise the cart will be twisted off the track as it is repelled by the magnetic disks; if the two pairs of disks, one pair on the cart, and the other on the bumper, are not properly aligned, the magnetic forces will be directed to the side instead of parallel to the track.
3. Data collection automatically ends after two seconds. Catch the cart before it returns and collides with the motion sensor.
4. When you are done, a negative spike on the force curve will appear (see Figure 1).
If the velocity data is irregular, it may be due to reflections off the track or some object nearby other than the reflector card.
The force acting on the cart during collision is negative because the magnetic bumper on the force sensor exerts a force in the negative x-direction (toward the sensor). Use the magnifying cursor at bottom left of screen (it has a + inside a circle) to expand and display the region of the spike (see Figure 2).
-4-
It is not necessary that the selected region include the entire duration of the collision. In case it doesn’t, the impulse measured (in Step 6 below) will be the impulse which occurred during that selected time interval, and Equation 1 will still be valid. Several different collisions will be made, and they all will have different measured impulses, corresponding to the different areas high-lighted each time by the student. However, if the student selects wide time-intervals for investigation, the experimental error associated with measuring the velocity (in Step 7) will be smaller than it will be for more narrow time intervals.
6. Use the statistics integrate option to find the area between the spike and the time-axis; note that this area will be negative because the force is negative. According to Equation 1, this area is the impulse delivered to the cart during the collision. Record this integral value in the table.
7. Use the cross-hairs cursor to line up the vertical hair with the left side of the high-lighted box (see Figure 3) then carefully move the cursor to meet the velocity curve to read the initial value of the cart’s velocity. Note that this value will be positive. Repeat this procedure for the right side of the high-lighted box to obtain the final (negative) velocity of the cart. Record the initial and final velocities in the table.
8. Calculate the initial momentum, the final momentum, and the change in momentum and record these values in the table.
9. Calculate the percentage difference between the integral of the force-time curve and the change in momentum.
10. Repeat Steps 2-9 three more times. Note: it is possible that the force sensor may become uncalibrated following a collision. Before collecting new data, check the calibration by collecting data without a collision to make sure that you still get a flat force curve at zero Newtons.
Mass of Cart m = kg // Trial 1 / Trial 2 / Trial 3 / Trial 4 /
v0 m/s
v m/s
mv kg m/s
mv0 kg m/s
Impulse
I = mv-mv0
kg m/s
Force-Time
Area = A
(Impulse) N-s
Percentage
Difference =
|(I -A)/I| x 100% /
Note: since a Newton (N) is the same as the units kg·m/s2, a N-s is the same as kg·m/s.
1