PHY 211 Lab 7 Worksheet

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Physics

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Apr 3, 2024

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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:

t = √ 2 h g Using the time elapsed for the ball to hit the ground (t) calculated above, we can calculate the expected distance (x) for the ball to fly over before it hits the ground after being ejected from the launcher from the initial velocity of the ball (v ball ). Because the horizontal component of velocity stays constant, and the ball is being launched completely parallel to ground, we can use the following equation: v ball = x t To solve for x: x = v ball t 3) Researcher(R3): the DA will provide some form of graph that shows the “random uncertainty” from the projectile launcher. However, the group introduced some “systematic uncertainty” based on how they made the measurements of masses, angles, and radius of the pendulum. In your personal copy of the excel data, adjust the values referenced by the equations to see which of the measurements have the greatest impact on the “predicted distances.” We are looking for statements like “The .5 (unit) uncertainty in XXX caused our predicted distance to change by about # . This 𝑐𝑚 (does/doesn’t) account for the differences between our predicted distances and the actual distances. What is the single largest source of uncertainty in your final results? Is this a “systematic uncertainty” or a “random uncertainty?” The .00005 kg uncertainty in mass of the pendulum caused our predicted distance to change by about 0.00027 m (0.027 cm). This doesn’t account for the differences between our predicted distances and the actual distances. The .0005 m uncertainty in height of the ball launcher caused our predicted distance to change by about 0.00033 m (0.033 cm). This doesn’t account for the differences between our predicted distances and the actual distances. The .0005 m uncertainty in radius of the pendulum caused our predicted distance to change by about 0.00115 m (0.115 ). This doesn’t account for the differences 𝑐𝑚 between our predicted distances and the actual distances.

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