Lab Report #1

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 ● 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

Range Vs Height Report Theory An object undergoes free fall when the acceleration is only due to gravity. This constant gravitational acceleration points towards the ground. The object may travel along a complicated two-dimensional path but its motion can be decomposed into two independent one-dimensional motions. Gravity acts only in the vertical (y) direction and therefore there is no acceleration in the horizontal (x) direction. Using this information, we can write expressions for the position and velocity of the object as a function of time. When the ball undergoes vertical motion, 𝑣 𝑦 = − 𝑔𝑡 𝑦 = 𝐻 − 1/2 𝑔𝑡 2 where H is the drop height of the object. When the ball hits the ground, 𝑦 = 0 𝐻 = 1/2 𝑔𝑡 2 (2H/g) 𝑡 = √ 7

Range Vs Height Report 𝑅 = 𝑉 0 𝑡 𝑅 = 𝑉 𝑜 √2𝐻/𝑔 Calculations and Results I. Measuring scatter in data Drop # Range Sum of Ranges Current Average 1 30.5 30.5 30.5 2 31 61.5 30.75 3 32 93.5 31.16 4 32.7 126.2 31.55 5 31.8 157 31.4 6 35 192 32 7 32 224 32 8 33.9 257.9 32.24 9 33 290.9 32.32 10 32 322.9 32.29 11 32.5 355.4 32.31 12 32 387.4 32.28 13 32.9 420.3 32.33 14 32.5 452.8 32.34 15 33.8 486.6 32.44 8

Range Vs Height Report 20 32.45 0.9 15 26.64 1.2 10 20.01 2.2 5 15.71 1.7 Figure 3. A graph plotted between the average range of the object and the drop plate height. 10

Range Vs Height Report Figure 4. A graph plotted between the average range of the object and the square root of the drop plate height. Discussion and Conclusions We found that the range of the object has a linear relationship with the square root of the drop plate height. This can be found from graph #2. The slope of the graph (1.53) is more consistent than the slope in graph #1 (0.802). Graph #1 plots the curve with the range of the object against the drop height while graph #2 plots the curve with the range of the object against the square root of the drop height. Furthermore, graph #2 corresponds to a straight line while graph #1 is a curve. This relates to the equation of the range of an object undergoing free fall and hitting the ground derived in the theory. 11