Lab 14: Impulse-Momentum Activity

Impulse-Momentum Lab 

I-Shou Lin, Kirk Paderes, Jorge Avalos

4/19/17

To measure, observe, and verify the impulse-momentum theorem

In the case of a cart on a track that's going to collide with an immobile surface, there's a force that acts on the cart which causes the cart to reverse its direction. However, since there're other net external forces that act on the cart during collision such as friction and air resistance, the collision is only nearly elastic. In the absence of all other net external forces, the collision is perfectly elastic, and the impulse momentum theorem is valid. We can verify that the impulse is equal to the change in momentum by plotting graphs of force versus time and velocity vs time, and then find the area under the curve of the graph of force versus time, and compare that integral value with the change in velocity multiplied by the mass. These two values should be equal or very close to each other. 

The entire lab is a collision experiment of nearly elastic and perfectly inelastic collisions. In the first experiment, we setup the rod clamped to a lab table with a cart attached to a rod and a track for the other cart with a force sensor mounted on that cart. It's setup so that the stopper of the moving cart hits the plunger of the stationary cart. Then, we ensured that the track is level, activated the motion detector, and calibrated the force probe. Finally, we collide the cart against the other cart several times until a good a set of graphs is obtained. Experiment 2 is just the same steps as experiment 1 except with several hundreds of grams of more masses. Experiment 3 is the completely inelastic collision in which the cart sticks to the wall. The cart attached to the rod has been replaced with a block of wood with a piece of clay attached to the front. The rubber stopper is replaced with a nail. We then collide the cart against the clay several times until we get the same initial velocity as the previous experiments. 

( Set up of experiment 1 with two carts)

( collision of experiment 3 in action)

Data Table

	Trial 1	Trial 2	Trial 3
Mass ( kg)	0.701	1.101	0.704
Velocity initial (m/s)	0.544	0.4593	0.500
Velocity final  ( m/s)	-0.395	-0.3255	0

Calculated Results/Graphs

( graph of position, velocity, and force versus time for experiment 1 with integral value)

( graph of position, velocity, and force versus time for experiment 2 with integral value)

( graph of position, velocity, and force vs time for experiment 3 with integral value)

	Experiment 1	Experiment 2	Experiment 3
Integral value (s*N)	0.8256	0.6318	0.3251

experiment 1 

Δp= p ( final)- p (initial)= m(v ( final)-v ( initial))= 0.701 kg* ( -0.395 m/s- 0.544 m/s)= - 0.658 kg*m/s

experiment 2 

Δp= p ( final)- p (initial)= m(v ( final)-v ( initial))= 1.101 kg ( -0.3255 m/s- 0.4593 m/s)= -0.864 kg*m/s 

experiment 3 

Δp= p ( final)- p (initial)= m(v ( final)-v ( initial))= 0.7011 kg * ( 0 m/s- 0.500 m/s)= -0.352 kg *m/s

All three experiments show the graphs of position, velocity, and force vs time. The position vs time graph shows us the movement of the cart relative to the motion detector. In addition, the slope of the graph is velocity. The velocity vs time graph shows the rate of movement before and after the collision when the velocity drops from positive to negative. The velocity is positive when the cart is moving towards the motion detector, and the velocity is negative when the cart is moving away from the motion detector. The abrupt drop in values corresponds to a high negative slope which is the time of collision. Finally, the force vs time graph is the key to verifying the impulse-momentum equation. The area under the graph of force vs time is equal to the impulse which is equal to the change in momentum as stated by the impulse-momentum equation. Therefore, if we take the integral of the graph of force vs time, we can get the impulse, and compare that value with the theoretical calculations for change in momentum.


Conclusion

In doing this experiment, we recorded data and graphed the position, velocity, and force vs time graphs on logger pro in order to analyze the impulse momentum theorem. Our graphs for all three experiments are consistent with theoretical predictions of what the general shape of the force vs time graph should look like before, during, and after the collision. The usual sources of error of friction and air resistance have a negligible effect on the motion of the cart due to its short time interval in reaching the end of the track and the minuscule interval of time of the collision. The calculated change in momentum of the cart didn't equal the measured impulse applied to it during the nearly elastic collision because of the inadequacy of the spring bumper and the execution of the experiment. The impulse and change in momentum were not equal to each other using more massive cart. I predict that that the impulse will be smaller than the impulse in the nearly elastic collision.The impulse and momentum will still be equal to each other. The force time curve for the nearly elastic collision stretches longer in time than the force time curve for the inelastic collision. The curve for the inelastic collision is very sharp and abrupt. This makes sense because there's only a small instant of time in which the force acts before the cart stops. Therefore, the curve should be high and thin, and it also means that the change in momentum won't be as great as compared to an elastic collision. In theory, the change in momentum should equal to the impulse or force multiplied by time. But, reality dictates that it's not the case due to human mishaps in conducting the experiment itself.