PHY 211 Lab 7 Worksheet

Lab #7: Momentum Worksheet 1) Researcher(R1): The researcher is responsible for explaining the above steps in detail. Special attention should be given each time mass is used in a formula to make it clear whether the mass is referring to “the mass of the ball”, “the mass of the pendulum” or “the mass of both.” In order to calculate the change in gravitational potential energy in excel, the below formula was used: Δ PE = PE i + PE f =( m p + m ball ) gΔH Where m p represents the mass of the pendulum, m ball represents the mass of whichever ball is being tested, and ΔH represents the change in height of the center of mass of the pendulum from its resting position to maximum height reached. Because the collision is inelastic, meaning the pendulum and the ball stick together after the collision, the masses were combined in this expression to represent this. Additionally, we were able to use this expression for the change in gravitational potential energy because we set y i =0 as the center of mass for the pendulum right before the collision (at rest), and ΔH represents the height change from y i =0 to y f =H as the pendulum swings up after the collision to its maximum height. Because initial height was zero, the value in for PE i would equal zero, so there is no need to include this in the equation. It is assumed in this experiment that energy is conserved during the collision, so we could say that: Δ PE = ΔKE This allowed us to find the change in kinetic energy of the system during the collision. Next, we used the following equation to determine p 1 , the momentum of the ball and pendulum together after the collision: p 1 = √ ¿¿ Which can be derived from the following equation by solving for p: Δ KE = p 2 2 ( m p + m ball )

Again, the mass of the pendulum and the mass of the ball being tested were combined because of this being an inelastic equation. Then, because momentum is conserved in all collisions, the momentum (p 1 ) of the ball and pendulum system after the collision will be equal to the momentum of the ball and the pendulum system before the collision (p 0 ): p 1 = p 0 Then, since initial momentum (p 0 ) is only considering the movement of the ball since the pendulum is stationary prior to the collision, the p 0 is equal to mass of ONLY the ball being tested times its initial velocity: p 0 = m ball v ball Velocity can be calculated by solving for v ball from the above equation: v ball = p 0 m ball 2) Researcher(R2): Explain with equations, how the measurements of height and angle of the projectile launcher produced the final result, the predicted distance traveled. Because the angle of the projectile launcher was 0°, this means it was horizontal to the ground, and therefore balanced. This results in it being easier to manipulate the horizontal and vertical components of the ball’s motion, since the ball will only have horizontal velocity once initially launched. From the height of the projectile launcher, we were able to calculate the time (t) it takes for the ball to hit the ground after being launched by using the following 1D motion equation for the y component only: y = v 0 y t −( 1 / 2 ) gt 2 Because the initial vertical velocity will be zero, we can omit the first term (v 0y t) on the right side of the equation. The height is negative in this instance (y=0 is where the bottom of the ball sits inside the launcher), so the following equation can be produced after substituting -h in for y: h =( 1 / 2 ) gt 2 Solving for t produces the following equation:

The .00005 kg uncertainty in mass of the ball caused our predicted distance to change by about 0.0065 m (0.65 cm). This doesn’t account for the differences between our predicted distances and the actual distances. The 0.25° uncertainty for the zero offset angle caused our predicted distance to change by about 0.082 m (8.2 cm). This does account for the differences between our predicted distances and the actual distances, and this is the single largest source of uncertainty in our final results as well. This is a systematic uncertainty, because it affects the measurements for all angles that the pendulum made at maximum height the same for all 5 runs of the 3 trials. 4) DA1: Include the entire raw data table for only one of the balls as well as the information at the top that was used in all trials. Raw Data- BALL TWO Trial Angle Δ H | Δ PE| | Δ KE| Pafter Collision Pbefore Collision V ball x Distance to target paper (m) 1 8.5 0.00313 0.007743302 0.007743302 0.062520549 0.062520549 2.963059171 1.331191176 2 8 0.006860556 0.006860556 0.006860556 0.058849033 0.058849033 2.789053707 1.253017057 3 8 0.006860556 0.006860556 0.006860556 0.058849033 0.058849033 2.789053707 1.253017057 4 8 0.006860556 0.006860556 0.006860556 0.058849033 0.058849033 2.789053707 1.253017057 5 8 0.006860556 0.006860556 0.006860556 0.058849033 0.058849033 2.789053707 1.253017057 5) DA2: Decide on a simple graphical method to represent the predicted distance and actual distance for all of your data. Thirty points on a graph will difficult to understand so make sure that you consolidate your data and take advantage of error bars to make the reader able to understand your data easily.

The graph, shown above, displays the average predicted distance vs. the average actual distance of each ball, 1 through 3. The averages of each were taken from trial 1 through trial 5 for each ball. The weight of the balls increased throughout; ball 1 is lightest and ball 3 is heaviest. It can be observed that the predicted distance was slightly higher than the actual distance for each ball. The error bars on each ball, predicted and actual, show the uncertainty in the experiment. The largest source of uncertainty was the zero offset angle. This systematic uncertainty affected the measurement of the angle when the pendulum reached its maximum height. 6) DA3: Create a caption for your Chart which explains in words what the graph means about your experiment. Mention the “single largest source of uncertainty” identified by the Researcher (in R3 above) and how that is integrated into the graph (or how it would adjust the graph if it is not yet a part of the graph). Located under the graph above. 7) PI1: Your ultimate goal is to address whether conservation of momentum and conservation of energy allowed the group to make accurate predictions of distance that