Lab Report 5

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EAS 104

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Physics

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Jan 9, 2024

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Phys 207 Lab CD1 Instructor: Luis A. Álvarez García Group: Lindsey Rosario, Ophir Amon, Brandon Bedoya, Shahi Shahnaj Report #5: Linear Momentum Lindsey Rosario Introduction The primary goal of this laboratory experiment is to validate the fundamental concept of linear momentum conservation. To accomplish this, we will utilize a steel ball, which will be granted an initial velocity by rolling it down a carefully designed incline. As the ball reaches the base of the ramp, it will subsequently collide with a wooden block, causing the ball to become embedded within the block. By examining the momentum of the system, both preceding and following the collision, we can assess whether the conservation of linear momentum holds true in this scenario. Procedure Step 1 : Finding the Centripetal Force with Weight Situate the wooden block on the platform. Take out the slider guide and slider from their container. Secure a waxed paper strip to the box's base using clamps. Release the steel sphere from the track's highest point, allowing it to roll downward. Watch as the sphere drops into the box and creates a mark on the waxed paper. Observe the horizontal position of the track's end, which enables basic kinematic calculations to estimate the sphere's velocity when exiting the ramp.

Lab 5: Linear Momentum Ascertain the height (b) through which the sphere descends, keeping in mind that the track is a channel and the lowest point of the sphere is beneath the channel's upper edges. Carry out a minimum of ten trials to gather suﬃcient data. Determine the average distance (d) the sphere covers before making contact with the ground, using the data collected from the trials. Step 2 : Calculate the linear momentum of the system Measure the mass of the steel sphere and note the mass of the wooden block Install the slider guide and slider within the box. Suspend the block at an appropriate height, ensuring its faces are parallel to the corresponding faces of the box and that it hangs freely, maintaining a 1/8-inch gap between the block and the track. Ensure the block remains completely stationary while waiting for the sphere's arrival. Measure the distance (h), taking into account that the suspension prevents rotation when the block swings. Measure the horizontal distance (x) the block travels after impact, and calculate the vertical distance (y) using the formula: y = h - √(h² - x²). Apply the conservation of energy principle to determine the velocity (v_b+m) of the block/mass system immediately after the collision using the equation: v_b+m = √(2gy). To find x, position the slider to barely touch the stationary block and record the distance setting from the slider guide. Conduct trial runs until the slider is optimally placed for ten successive impacts, where the block sometimes just ﬂicks the slider and sometimes barely misses it. Note the slider's position and calculate x. Determine the linear momentum of the system before impact (mv_b) and after impact ([m+M]v_b+m), and calculate the percentage difference between them. 2

Lab 5: Linear Momentum Data and Calculations Experiment 1: b= ball drop distance = 13cm+/-0.005cm = 0.13m d= distance ball travels = 29.06cm +/-0.005cm = 0.2906m Ten trials: Trial number: Distance traveled (d): 1 22.0 cm 2 23.2 cm 3 27.0 cm 4 28.0 cm 5 29.0 cm 6 34.5 cm 7 38.2 cm 8 28.5 cm 9 26.2 cm 10 39.0 cm Average d= 29.06 cm = 0.2906m Uncertainty= +/-0.5cm=0.005m Error using the standard error method= 0.019m Experiment 2: (where m b is mass of ball and m w is mass of wood block) m b = 66.8g= 0.0668kg m w = 81.5g= 0.0815kg m b +m w =0.1483kg 3

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Lab 5: Linear Momentum h= 40.8 cm +/- 0.005cm x= 16.6 cm +/- 0.005cm Y = 0.408 - √0.408^2 - 0.166^2 = 0.0353m v b+w =√2gy = √2*9.8*0.0353 =0.8318 m/s d=mv i +1/2gt^2 0.166=4.9t^2 t=0.18406s v b =d/t=0.166m/0.18406s=0.9019 m/s Velocity uncertainty: 0.773 m/s Questions 1. How do multiple measurements of d change the uncertainty? Compare the uncertainties in the velocity of the ball using these two different methods. a. By utilizing the original method to calculate uncertainty, we obtain a 0.005m uncertainty for d. When employing the standard deviation method, the uncertainty for d is found to be approximately 0.019m. These values are quite similar. However, the standard error provides a more precise error, thus displaying how the standard error method yields more accurate results. Regardless of strategy, having more values of d (doing more trials) helps to better encapsulate and calculate the error. In the case of velocity, we have a 0.5m/s uncertainty with the conventional method and a 0.773 m/s uncertainty using the standard deviation technique. Once more, the values are close, but the standard deviation approach yields a more accurate error estimate. 4

Lab 5: Linear Momentum 2. Within the limits of your experimental accuracy, is momentum conserved during the collision? a. From our data, it is observed that momentum is conserved because when the ball collides with the wooden block, its force causes the ball and wooden block to move in the same direction, at the velocity appropriate for the mass of the wooden block. After the collision, the two items move together as a system of objects instead of individual things, displaying how momentum is conserved and shared between the objects. However, due to human error, these factors can be tampered in a way that harms the accuracy of final results. 3. Derive equation (1), starting from general physics principles. a. What equation? Please explain. 4. From your results, compute the fractional loss of kinetic energy of translation during impact. Disregard rotational energy of the sphere ??? 5. Derive an expression for the fractional loss of kinetic energy of translation in terms only of m and M, and compare with the value calculated in the preceding question. Consider the collision as a totally inelastic one. Kinetic Energy Loss = (½ mv2 - ½(m2/m+M)v2)/½ mv2 5

Lab 5: Linear Momentum Conclusion In conclusion, the laboratory experiment conducted has successfully validated the fundamental concept of linear momentum conservation. By utilizing a steel ball that was given an initial velocity by rolling it down an incline and colliding with a wooden block, we were able to examine the momentum of the system before and after the collision. Through careful observation and analysis of the data collected, we were able to confirm that the conservation of linear momentum holds true in this scenario. This experiment serves as a crucial reminder of the importance of understanding the fundamental principles of physics, and how they apply to real-world scenarios. It is important to continue conducting such experiments in order to improve our understanding of physics and how it can be used to solve practical problems. References Lab Manual 6

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