9- Oct.- 2014 Momentum/ Impulse Lab

Momentum Lab

Partner: Adam Moro

Objective: 

  Show that in each scenario (both elastic and inelastic collisions) that momentum is conserved .

Set Up:
There are three set ups:

Figure 1. A set up very similar the first set up (except the extra mass)

1) We use a track and a cart with a force sensor attached to the top of it, another cart that is stationary with a springy bit extended. A motion sensor is on the opposite end of the track reversing the settings in the motion sensor so it read motion toward it as positive. You must collide the movable cart with the stationary one and record your data.

2)Repeat the first experiment, but add a 500 g weight to the movable cart.

Figure 2. Our second set up has an extra half a kg
to increase the amount of impulse in the system

3) Replace the stationary cart with a platform with molding clay on it. Attach a nail to the end of the force sensor and collide.

Data Collection:
  With each experiment with its own objectives each had a very similar approach. For each we had to find the impulse or change in momentum (p) which means there are things we have to consider:

• Since friction in this case is negligible and the surface is level, the amount of net force just before collision in each case is 0N
• The point when the cart is experiencing maximum linear force is during impact at instantaneous rest
• There is no net force after impact acting on the cart
• As we will see later, since m*vf - m*vo=  F*t where t is the how long a collision took place, it varies in different scenarios

As seen below in (fig 4) we use data such as initial and

final velocity from the collision, collision time interval

Figure 3. Our cart now has a nail at the front meant to stick
into a wad of modeling clay for an inelastic collision.

and maximum force experienced during the collision. We then compared the theoretical calculations to the actual results with calculated error for each in percent. Where we got the numbers we used for these calculations will be on the next few figures.

Figure 4. Lab Calculations for each experiment with theoretical answers compared to
actual using known mass and given velocities from our results.

  Experiment 1

Figure 5 A and B. Data recorded from experiment 1 including the integration of total impulse, highlighted time interval of collision and velocity values used for theoretical calculation of impulse in this experiment.

Here we used a cart of a known mass of .43 kg. As the figures show, velocities right before and right after collision are .834 m/s and -.759 m/s respectively with a impulse of -.7389 N*s (slightly different than on notes) and a collision time interval of .12s both considerably higher than the calculated -.685 N*s and .1s, but overall the behavior of the graph does suggest conservation of momentum seeing as the graph reaches a peak at close to instantaneous rest and returns with a close to zero net force. Any loss in momentum may have been caused by the friction in the spring of the fixed cart.

Experiment 2:

Figures 6A and B. Data recorded from experiment 1 including the integration of total impulse, highlighted time interval of collision and velocity values used for theoretical calculation of impulse in this experiment.

Here we used a cart of a known mass of .43 kg, but we added another .5 kg to see if the system is conserved once more in a elastic collision. As the figures show, velocities right before and right after collision are .464 m/s and -.401 m/s respectively with a impulse of -.8591 N*s and a collision time interval of .18 s (longer than the previous trial due to the increase of the moving cart's mass) but both are considerably higher than the calculated -.8044 N*s and .13s, but overall the behavior of the graph does suggest conservation of momentum seeing as the graph reaches a peak at close to instantaneous rest and returns with a close to zero net force. Any loss in momentum may have been caused by the friction in the spring of the fixed cart and friction in the wheels of the moving cart due to the increase in load. 

Experiment 3:

Figures 7A and B. Data recorded from experiment 1 including the integration of total impulse, highlighted time interval of collision and velocity values used for theoretical calculation of impulse in this experiment.

Here we used the same cart of a known mass of .43 kg, but instead added a nail the end of its force sensor. As the figures show, velocities right before and right after collision are .861 m/s and 0 m/s respectively suggesting an inelastic collision with a impulse of -.3178 N*s and a collision time interval of .12s both considerably higher than the calculated -.370 N*s and .05s, this may be due to the slight struggle of the cart trying to escape the clay causing a small time of positive force before coming to a rest thus elongating the time before the cart is at rest. However, it does seem that momentum is conserved seeing as how it acts very similiar to the other two previous trials.