Lab Report - PHYS 170

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Leeward Community College *

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MISC

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Physics

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Feb 20, 2024

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Lab 2 Report Forces, Motion, and Graphs

Objective The objectives of this lab are to: ● Determine the relationship between force and acceleration ● Create a graph of position ● Create a graph of velocity ● Determine the acceleration of an object Materials For this experiment, we used: ● A round ball (resin textured) ● Ruler ● Camera (Phone, tablet, or laptop) ● Movie Playing software ( https://physlets.org/tracker/ ) ● Protractor ● Ramp made out of cardboard (3 foot display board) ● Two pillows (to prop the cardboard up) ● OPTIONAL: Bribe (Just for someone to release the ball down the ramp while recording) Theory Explain the theory of the lab. Don’t copy what is written. Talk about the forces involved and the graph that we made and how we are getting the acceleration from the graph. In this lab, the forces acting upon the ball will be gravity and normal force. Gravity and normal force affects the ball when it rolls down the ramp. Normally friction would be present, but in this lab it will be ignored. To find the acceleration of the graph, the motions of the graph are analyzed. A tracker program was provided and used to analyze the line of the graphs and motions of the ball as it was rolled up and down the ramp. Three separate graphs were made and each graph had a slope that was used to find the acceleration. In the graph of position vs. time (the top graph of each pair) the slope is the velocity. While in the graphs of velocity vs. time (bottom graph of each pair) the slope is the acceleration.

Method In this lab we constructed a ramp from a cardboard display board and a pillow acting as a prop for the cardboard to rest on. We measured the angle we needed with a protractor and adjusted accordingly, leaning the ramp higher or lower on the pillow. We measured the height of the ramp, length of the cardboard, and length of the cardboard along the floor. Then we rolled the ball down the ramp for each part and set up the camera to record videos for each part for the tracker program. For the tracker, we put the calibration stick tool on the ramp. The calibration stick is used to tell the program the scale of the video. We tracked the ball making sure we used the center as the tracking point. Afterwards, we used the data tool to analyze the position and velocity. We were able to calculate the slope of the velocity graph using the data tool. PART 1 & 2: Lower Angle

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PART 3: Higher Angle Data PART 1 DATA: Slope angle, θ (°) =14° (optional) height of ramp (m) = 5.5 inches, 0.1397 m (optional) ramp length along floor (m) = 34.75 inches, 0.88265 m (optional) slope angle = tan -1 (height/ramp length along floor)= 0.2125668 Calibration length (m) = The length of the board? (35.5 in) acceleration observed (slope of v vs. t) (m/s 2 ) = 0.8518 m/s 2 theoretical acceleration = g sin θ (m/s 2 ) = 2.37m/s 2 (note g = 9.81 m/s 2 )

PART 2 DATA: Slope angle, θ (°) = 14° Calibration length (m) = 35.5 in, acceleration observed (slope of v vs. t) (m/s 2 ) = -0.8809 m/s 2 theoretical acceleration = g sin θ (m/s 2 ) = 2.37m/s 2 (note g = 9.81 m/s 2 ) PART 3 DATA: Slope angle, θ (°) 18.9° Calibration length (m) = 35.5 in, acceleration observed (slope of v vs. t) (m/s 2 ) = 1.310 m/s 2 theoretical acceleration = g sin θ (m/s 2 ) = 3.18m/s 2 (note g = 9.81 m/s 2 ) PART 1 GRAPH:

PART 2 GRAPH: PART 3 GRAPH:

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Calculations To find the angle of the first ramp we calculated and found: arcsin(11.5/35.5) = 18.9 degrees To find the angle of the higher ramp we calculated and found: arcsin(5/35.5) = 14.1 degrees Analysis 1. Find the % error for each of the three parts above. Percent error = |observed-theory|/theory*100% - Part 1. PE= |0.8518 m/s 2 -2.37m/s 2 |/2.37*100%= 64.06% - Part 2. PE= |-0.8809 m/s 2 -2.37m/s 2 |/2.37*100%= 62.83% - Part 3. PE= |1.310 m/s 2 -3.18m/s 2 |/3.18*100%= 58.81% 2. Are there any systematic errors in this lab? If so, list them. If not, explain why not. - The systematic errors that we had in our lab was that one of our group members had to use three to four rulers instead of a tape measure to get the measurements for data. Another error could be that when we were using the tracker website, it was difficult to try and pinpoint exactly where the middle of the ball was since the ball was in motion and as it moved frame by frame it made it difficult as it was getting blurry. Lastly, the device that was being used to video the lab of the ball in motion was not properly straightened. Instead, there was a minor crookedness to the video that was not noticeable, unless it was being rewatched over and over again. Conclusion Did you fulfill all of the objectives of the lab? Were you successful in proving or disproving your hypotheses? Explain how you have achieved these things. (Theoretical hypothesis is the hypothesis) - Within our group, we were able to fulfill the objectives of the lab based on the materials that we were given, we were successful in accomplishing the tasks of finding forces and motion on a given object. A website was given to us to make it easier for us to find points and convert the data into our velocity and position graphs. Then, based on the information that the graphs and tracker website gave, we identified and determined the acceleration of our object and saw the relationships between motions and forces. That being said, we can conclude that hypothesis (theoretical acceleration) was not correct because due to our percent errors, each of the parts for the lab were over or near 60% of error within our lab. But, granted, we ignored the fact that there was friction and that

our ball was on the bigger and heavier side. So, based on all of this, we made the objectives, but sadly were not able to prove our hypotheses. Q UESTIONS 1. Why is there no difference in theoretical acceleration in Part I and Part II? (Hint: think about the forces.) - There is no difference in the theoretical acceleration in Part I and II because none of the forces that were being acted upon changed. Instead the only thing that was different between part I and II was the initial direction that the ball was heading. The theoretical acceleration should be the same throughout these parts due to all of the factors being the same and that there is a little more motion in part II since the ball has to go up and come back down and it is going the opposite direction, but forces on the ball are still equal to the forces in part I. 2. In part II, you might have recorded a negative acceleration. Why might you record a negative acceleration? - The reason why we recorded a negative acceleration is because since we had to roll the ball (or object) up the ramp, it was heading towards the negative x-direction, if we are imagining an x and y axis. Unlike parts 1 and 3, it was rolling down the ramp and was heading or rolling in the positive x-direction. Hence, this is why we recorded a negative acceleration for part 2 of this lab. 3. We assumed that friction was minimal. Depending on your ball, this may or may not have been a good assumption. If friction is added to the analysis, would it have increased or decreased your theoretical acceleration? Explain. - If friction was added to the analysis, then we think that it would have increased our theoretical acceleration due to the fact that the ball we used was on the heavier side. Since the ball is heavier there would be more friction, the added friction caused by the ball's weight would have increased our theoretical acceleration and as a result make our percent error decrease. 4. Considering the % difference you observed, was friction a significant factor in your experiment? (Meaning, do you think that if you’d truly had a frictionless system you would have been able to see a difference in the measured acceleration or is the effect small enough that random uncertainties could account for the difference you observed?) This is just your guess but explain your reasoning. - Considering the percent difference that is observed, friction is a big factor in any experiment. However in our experiment, due to the weight of the ball that was used

being on the heavier side the friction would be greater as it would be more force upon the object. Since that is more weight, resulting in more friction that was not taken into account initially in the experiment, the percent difference would be greater.

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