Lab 14 - April 20, 2015 - Physics 4A Impulse-Momentum Activity

Lab 14:
April 20, 2015
Brandon Elder

Physics 4A Impulse-Momentum Activity

Purpose: To show that the impulse can be calculated as the area under the force vs. time graph and that the impulse applied to an object equals the change in momentum of that object.

Definitions:
Impulse combines the applied force and the time interval over which that force acts. The impulse: J is J=F(change in t). On a graph plotted for F and t this would look like the area under the graph. Therefore the impulse is the area under this graph. The area under the graph will equal the the impulse for a constant applied force and for a varying applied force.

Impulse applied to an object equals the change in momentum of that object, in one dimension,
J = change in p (momentum) = Integral of F * dt.

Set-Up: Arrange equipment and apparatus to reflect the image shown in Fig. 1. Perform all calibrations and zeros accordingly for the motion detector and the force sensor, as per all previous labs. It is important to note that during the set up you want to ensure that the stopper of the moving cart hits the plunger of the stationary cart when the moving cart gets close to the end of the track.

Fig. 1 Set up of apparatus. Cart, with a shield attached to let the motion detector know where it is, a force sensor mounted sideways on top of the cart, a mounted cart with a springy bit, and a track for the unmounted cart to roll on. 

Experiment 1: This first experiment will be quick. With logger pro recording data and a graph of force vs time displayed, observe and record. The graph will show that the force is not constant and that the collision is not an elastic collision. Some things to note before recording the official data would be to make sure that the cords are not going to be interfering with any of the readings as this would skew the data. Remember to calibrate the force sensor holding it vertically then to zero the sensor when it is attached horizontally. Practice pushing the cart toward the plunger and watching it bounce to observe the best possible positioning and placement. Zero the force probe and begin graphing. Once you hear the click, give the cart a push towards the mounted plunger, observe as it collides. The resulting graph should look like Fig. 2.

Mass of the Cart with Force Probe: 0.74 kg

Fig. 2 The graph of the first experiment. Here the area under the force vs. time graph is equal to 0.4065

The collision process takes less than half a second as you can see from the graph. The force exerted on the sensor just before and after the collision is zero. The magnitude of the force on the cart is maximum when it is collided the fullest with the spring plunger.

According to the impulse momentum theorem, the Integral of F * dt equals the mass * (velocity final - velocity initial).

Therefore the area under the graph above, 0.4065 should be VERY close if not equal to the difference in our velocities before and after the collision multiplied by the mass.

The velocity difference from before and after the collision multiplied by the mass of the cart is 0.4514. These numbers are very close to each other and this experiment proves that the impulse momentum theory is correct.

Fig a2 The mass of 500 g was added to the cart.

Experiment 2: For this experiment we collected data similar to above but this time we added weight. We added 500 g to the cart (see Fig a2).  The total new weight of the cart was: 1.24 kg. The cart was collided against the spring plunger and the graph was collected, (see Fig. 2 below). We ran two trials and both times the numbers were almost equal and only a few hundredths of a decimal place off. The second trial resulted in an area under the graph of .7156.

Fig. 2 The area under the graph of force vs. time for the larger mass on the cart was 0.7156. The velocity graph was used to determine the velocity before and after the collision. 

The velocity before collision reading: 0.318 m/s

The velocity after collision reading: -0.265 m/s

The difference of those two values multiplied by the mass of the cart is equal to 0.72292. As you can see, that is a difference of only 0.00732 or about a little more than a 1 percent difference. The experiment again goes to show that the impulse-momentum theorem holds true to a larger weight being placed on the cart. 

Experiment 3: This experiment will now show that the theorem holds true for an inelastic collision. The experiment will remove the spring plunger from the side and replace it with a block of wood that has a chunk of soft clay attached to the wood. There will be a nail placed on the edge of the cart and it will stick into the clay when the cart is released. The experiment was ran and the following data was collected:

Area under the graph: 0.5709 N*s

Velocity before collision: 0.428 m/s

Velocity after: 0 m/s

Mass of cart (with nail added) 1.253 kg

The difference in velocity multiplied by the mass in the cart is 0.536 and the area under the cart is .5709. This time the resulting numbers are off by around 5 to 6 percent. This margin of error has increased since the last experiment. However, the answer is still in the ball park and once again shows us that the theorem is correct.

Fig. 2 The area under the graph of force vs. time for the larger mass on the cart was .5709. The velocity graph was used to determine the velocity before and after the collision. 

Conclusion:

The numbers were not exact, but within 1 percent during one of the experiments so that is close. The object of the experiment was to show that the impulse-momentum theorem (as stated earlier) is true. We ran tests of a cart