Lab Report #1

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Physics

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Jan 9, 2024

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Range Vs Height Lab Report Course: PHYS 141-002 1

Range Vs Height Report Abstract We attempt to study the relationship between the horizontal distance, known as the range and the height at which the object is launched under free fall when the acceleration is only due to gravity. We analyzed the projectile motion of an object after it comes in contact with a bounce plate. We found that the range of an object is directly proportional to the square root of the height at which it is launched. Introduction In this lab, we achieve the objective of studying the range as a function of the height, the projectile motion of the object, and errors in the measurements through three different experiments. In the first experiment, we measured the scatter in the data we collected in terms of the position of impact of the ball against the table. The second experiment explores different methods to release the ball to the bounce plate and minimizes the errors in our measurements. We establish the relationship between the range and the height of the ball in the third experiment. 2

Range Vs Height Report Procedure I. Measuring scatter in data When making a measurement, it is important to be both accurate and precise. For example, if you measure the length of the room several times and get the following results, 10.64 m, 10.65 m, 10.64 m, 10.63 m, and 10.64 m, you would say this is a precise measurement because the variation between the different measurements is only ±0.01 m. However, if I told you the room was actually 11.00 m long you would know that your measurements were not very accurate. Similarly, if you measure the length of a meter stick 5 times and got the following results, 0.90 m, 1.10 m, 0.80 m, 1.20 m and 1.00 m you would say the measurement is not very precise because there is a large variation between the measurements. However, the average of all your measurements is exactly 1.00 m, which is the correct value. So, the average of the measurements is accurate. The goal of any experiment is to have both accurate and precise measurements. In this lab, we will be exploring ways to quantify the uncertainty in our measurements and how to improve them. In the first part of the lab, we will be dropping balls and measuring their final position. Each additional drop of the ball should reduce the uncertainty in our measurements. ● Set up the bounce plate so that it is 20 cm above the table. 3

Range Vs Height Report ● Set up the drop plate so that it is 20 cm above the bounce plate and directly above it. When it is properly aligned, a ball will fall through the drop plate, hit the bounce plate and then land on your table. ● Place a large sheet of newsprint on your table where the balls will land. ● Put a piece of carbon paper above the newsprint so that when the ball hits it, it leaves a mark indicating the location of the ball. When everything is set up properly, it should look like the picture below. 4

Range Vs Height Report II. Minimizing errors To get as accurate of a measurement as possible, you want to reduce the standard deviation in the data. In this section, you will explore different methods of dropping the ball to get the minimum standard deviation. ● Try a different way of releasing the ball from the drop plate. Some suggestions are using a ruler underneath the ball to hold it in place and then slide it away. Use the magnet to hold the ball and then move the magnet away to let the ball fall. Or come up with your own method ● Drop the ball 18 times for two different methods (This will give three methods in total with the first part of the lab). By looking at the spread of the landing spots, graphically determine the standard deviation for each method. You should use whichever method gives the smallest standard deviation. III. Determining range versus height In the rest of the lab, you will determine the relationship between the range of the ball and the height from which it is dropped. The range of the ball is given by the horizontal distance that it travels. It depends on both how far the ball falls before hitting the bounce plate and how high the bounce plate is from the table. We will 5

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