Newton’s laws of motion-conceptual

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Mechanical Engineering

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Jan 9, 2024

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Newton’s laws of motion-conceptual Goals The goal of the experiment is to observe Newton’s laws in action as well as to validate and/or refute the laws. Another goal is to be able to collect data and analyze it in Excel as well as being able to understand the data from graphical representations. Procedure To start the experiment a motion sensor was connected to the computer. A blue or black color on the sensor would give different instructions on how to perform the tasks. A black motion sensor would mean to plug the yellow plug into channel 1, the black plug into channel 2 and to set it as motion sensor II in the capstone hardware setup. The range would need to be switched to the wide beam setting. If a blue sensor was noted, it would need to be plugged into the computer and checked that the sensor is in the hardware setup menu. The range of the sensor would need to be set in the wide beam setting as well. The sensor was then aimed downwards so that the beam would hit the puck without picking up background data. As the record button was clicked, the hands were moved toward and away from half a meter from it to test to see if the data recorded had smooth increases and decreases in speed. For the actual test, one hand was used to push and release the puck in the direction of the motion sensor, traveling for about 20 cm, stopping it with the other hand. For Part II of the experiment, a modified Atwood’s machine was used. At the beginning of the experiment, the cart, the track, and the pulley were checked to make sure that they were all in the correct position for the weight to pull the cart over the pulley. The Capstone software was used to measure the velocity values of the cart. More mass was added to the cart and the velocity was measured. The third part of the experiment was set with two carts facing away from each other with only force sensors attached. By pressing the “zero” or “tare” buttons, the sensors were set to zero. Using the Capstone software, the sensor was set to record at least 5,000 samples a second. One of the carts had weight added to it so it would double that of the other cart. As the recording started, one of the carts was pushed into the second cart and the recording ended. The mass was then removed, and the procedure happened again. Error and Precautions There may have been some issues during the experiment because of both human error as well as an error that could not be avoided. When working with sensors and on computers, there is a chance that some of the technology being used did not work. Another source of error could have been the friction from the tires of the cart and the track which could have affected the velocity of the different objects being pushed.

Human error is something that is hard to avoid with the fact that pushing was a big aspect of the lab. The force acting on the carts or the pulleys may have had an impact on how different the velocities were as well as not being able to stop at a consistent 20 cm in the first part of the experiment. Results Part I

Part II m1 = Mass of cart = 254.8 g m2 = mass of weight + hanger = 20 g

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PART III Unequal mass PART III Equal mass

Questions Question 1. Which of Newton’s Laws describes the hover puck’s motion in region C? Newton’s first law of motion is where an object in motion will stay in motion with the same speed and direction unless acted upon by an external force. Question 2. Which of Newton’s Laws describes the hover puck’s motion in region A It is also Newton’s first law of motion stating that an object at rest will remain at rest unless acted upon by an external force. Question 3 . What does the value of the slope represent in our graphs of velocity vs. time It means that as the time increases the velocity will remain the same unless acted upon by an external force which happened at 9.8 seconds and caused the velocity of the puck to decrease. Question 4 . It’s very likely that the actual acceleration of the cart was less than the theoretical value you calculated. Do you think including friction in our theoretical analysis would bring our predicted value more in line with the actual value we measured or would including friction make our theoretical value even farther from what we measured? A brief qualitative answer is all that’s needed here. Incorporating friction into the equation would give a more accurate answer but there would be so many different values that would need to come into mind. It would not just be the friction of the wheels on the track but also the different axels in the cart itself. While looking at the track and the cart wheels, there would not be much friction lost as both are very smooth surfaces. Question 5 . What is the maximum acceleration of the system if you were to hang an infinitely large mass from the string? Hint: plug 1000 kg in for m2 and 1 kg in for m1. (It may seem surprising that large hanging masses don’t translate into large accelerations but remember gravity is providing the downward force!)

m1 (mass of cart) = 254.8 g = 0.2548 kg m2 (mass of weight + hanger) = 20 g = 0.02 kg Net Force = F_gravity(m2) - F_gravity(m1) F_gravity(m2) = m2 * g F_gravity(m1) = m1 * g F_gravity(m2) = 0.02 kg * 9.81 m/s² = 0.1962 N F_gravity(m1) = 0.2548 kg * 9.81 m/s² = 2.4995 N Net Force = 0.1962 N - 2.4995 N = -2.3033 N -2.3033 N = (m1 + m2) * a -2.3033 N = (0.2548 kg + 0.02 kg) * a -2.3033 N = 0.2748 kg * a a = -2.3033 N / 0.2748 kg ≈ -8.37 m/s² Question 6. As the hanging mass m2 is falling towards the ground, many people would guess that the tension in the string decreases, but this is incorrect! In fact, the tension remains constant over time. Prove that the tension remains constant over time as the mass is falling using Newton’s 2nd Law. To do this, draw a free body diagram of the hanging mass and note there are two forces acting on it: the tension and the force of gravity. Then use this to write out Newton’s 2nd Law for the hanging mass and explain how this shows that the tension is constant given that the acceleration is constant. ΣF = m2 * a ΣF = T - m2 * g T - m2 * g = m2 * a T = m2 * (a + g) Since a and g are both constants as well as the sum we can conclude that the tension in the string is constant over time as the mass falls because the force on it is constant due to the constant acceleration. The tension does not decrease as the mass falls. Question 7. Which of Newton’s Laws is explored in Part III of this lab?

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Newton’s third law is explored as it states, “ for every action, there is an equal and opposite reaction”. When the carts collide and the sensors are used to measure the forces, the experiment shows their relationship as different forces. Question 8. Imagine a large truck collides with a much less massive shopping cart. Which of the two has a greater force acting on it? The shopping cart has a greater force acting upon it because of the larger mass of the truck. Discussion The trial technique framed in this lab report included a progression of estimations and perceptions utilizing movement sensors, trucks, and computer software to examine the standards of movement. In the initial segment of the trial, the movement sensor was used to record the movement of a puck. The normal outcomes were smooth increments and a decrease in speed as the hands moved the puck towards and away from the sensor. It was normal that the sensor would precisely catch these progressions moving. In any case, the genuine outcomes might have caused problems from the normal experiment because of different elements, including sensor adjustment, situating, and other external obstructions. In Part II the Atwood's machine was utilized to measure the speed of a truck as mass was added to it. The normal result was that as more mass was added, the speed of the truck would diminish, reliable with the standards of Newtonian science. The outcomes show this converse connection between mass and speed. In Part III, the power sensors were used to measure the effect of power between two carts. The normal outcomes were that the power sensors would catch the powers applied during the impacts and that the recorded information would give experiences into the connection between power and mass. To survey the wellness of the outcomes, it is essential to inspect the information gathered and decide whether it lines up with the hidden actual standards. Without a trace of explicit information or charts, making an immediate evaluation of the fitting results is testing. In any case, the wellness of the outcomes can be assessed by thinking about whether they adjust to the

normal patterns and examples in view of the known material science standards. Any huge deviations from expected results should be investigated, assessed, and fixed. The trust in the outcomes relies upon a few elements. First, the exactness and accuracy of the estimation instruments, like the movement sensor and power sensors, should be accurate because they were expertly made and made to be exact. If these instruments were aligned incorrectly or were mistaken, it could influence the trust in the information. Furthermore, the consistency of the exploratory technique across preliminaries and the treatment of factors also influence certainty. Repeating tests and acquiring comparable outcomes would increase trust in the discoveries. A few likely mistakes were found in the trial. These are issues with the hardware, erosion between the truck tires and the track, and human errors related to pushing the trucks and stopping them reliably at 20 cm. Mechanical blunders might have impacted the precision of the sensor readings. Grating might have presented methodical blunders, prompting disparities in speed estimations. Human mistakes in applying power and halting the trucks at a particular distance could have presented varieties in the information. Generally speaking, it is important to recognize these possible mistakes and consider what they might have meant for the outcomes. It is additionally important to recommend upgrades or alterations to the exploratory arrangement to solve these problems in the ongoing cycles of the examination.