Physics lab report 1 - Understanding sensors - bungee jump lab PDF

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Understanding sensors - bungee jump lab ...

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Lab #1: Bungee Jump Anna Hofbauer, Misheel Dolguun, Dr. Schuler Introduction The purpose of this experiment is to gain an understanding of how different sensors are used, and how to collect and analyze the data obtained. The sensors utilized in this experiment were applied to a falling object attached to an elastic cord. From the data provided by the sensors, comparisons are able to be made between the results from each sensor. These comparisons allow for the understanding of how the sensors differ, and provide knowledge for future experiments using sensors. The “high resolution force sensor” is the sensor placed above the falling object. The sensor has two metal plates that are connected by a force sensitive resistor. When the resistor is affected by stretching or compression, the amount of current that flows through it changes as a result. The measured change in current can be calibrated and force measurement (Newtons/N). Because the sensor can only record the force of an object pushing or pulling on the attached hook, the bungee jumper (object) must be attached to the hook via an elastic cord so the object may pull on the sensor. The “ultrasonic motion detector” is able to measure the distance to an object repeatedly over a time frame. This data provides information on change in position and subsequently, velocity and acceleration. This sensor utilizes a speaker that emits high-frequency sound waves that bounce off the object, and are reflected black into a microphone built into the device. The sensor calculates distance by measuring the time it takes for sound to be reflected back. The Capstone Software is a program that collects real-time data, and was utilized in this experiment to record the raw data. Using the data, this program allows for mathematical functions to be applied for further data analysis and make graphs. The program also helps with determining analytical relationships in processes examined in the experiment. Bungee Jump Set Up A ring stand was attached to the side of a table, and the high resolution force sensor was secured to it. An elastic cord was attached at one end to the force sensor, and at the other, the bungee jumper (object), so that the bungee jumper was hanging from the force sensor. The ultrasonic motion detector was placed on the floor, directly below the bungee jumper; the force sensor, object, and motion sensor formed a vertical line. Using a meter stick, the object was lifted to a certain height and then dropped. Fig. 1 bungee jump set up

Trial 1 Position vs Time graph

The point where the elastic started slowing the jumper was (2.300 s, 1.64 m). The lowest point of the fall was (2.4 s, 1.37 m). The total distance the elastic stretched was 0.27 meters. The largest change in position and time was 2.52 m/s, and the smallest change was 0.11 m/s; these values indicate values for the velocity of the bungee jumper. Acceleration during Freefall

The average acceleration during free fall was -5.54 m/s^2. Velocity during Freefall

The linear equation representing the velocity of the jumper in free fall is v=-8.43t + 16.5.

Acceleration during Elastic Stretch Period

The curve of the acceleration of when the elastic band started stretching to when the jumper reached the bottom of it’s fall. The relationship is described by a=230t -526. Velocity during Elastic Stretch Period

The fitted curve of the velocity of when the elastic band started stretching to when the jumper reached the bottom of it’s fall. The relationship is described by v=18.1t - 44.2.

The beginning of the graph shows a fairly linear trend, but the values are unstable, indicating that the device may have not been completely secure and that there may be some error that is affecting the process of the bungee jumper falling. There are large dips in the force values of the graph, and these dips decrease in size as time progresses. These dips indicate regions where force is being exerted onto the object as the elastic band is stretched when it is dropped. The object eventually comes to rest, which is represented as a linear line. The jumper is in free fall until it reaches the point of (2.350 s, 5.518 N), and from there the elastic band is stretched until the object reaches (2.400s , -5.499 N), which is where the maximum force of 5.499 Newtons is exerted onto the jumper.

A linear line was fitted to this function. The function fits well to the area where the rubber band was stretched. The problem is that the values for the linear relationship have very large uncertainties. The equation for this function is N=-123t + 291. This function gives us the relationship between how much the elastic band was stretched and the force exerted on the jumper. Force, Acceleration, and F/A Plotted

F/A during Elastic Stretch Period

The mean value while the elastic is being stretched is -0.6 N/(m/sec2 ). According to Newton’s second law of motion, F=ma, the Force divided by the acceleration will result in the mass of the object. The object’s mass is 0.36 kg. Force multiplied by Time during the Elastic Stretch Period

The area under the curve during the elastic stretch period is equal to the force multiplied by time during that time frame. Total area = 4.805x10^-4 N⋅s. Velocity change during this time period is -1.87 m/s.

Trial 2 Position vs Time Graph

The bungee jumper was in free fall from 2.675s - 2.825s and the elastic was being stretched from 2.825s - 3.050s. At 3.050s the bungee jumper reaches its lowest point with the elastic being

stretched a total distance of 0.57m. The largest change in position/time was 7.92 m/s, and the smallest change in position/time: 0.15 m/s. Acceleration during Free Fall

The average acceleration in this time frame is -8.58 m/s2 . Velocity during Free Fall

The line of best fit for the velocity of the bungee jumper during free fall: v = -12.8t + 34.2.

Velocity during Elastic Stretch Period

Acceleration during Elastic Stretch Period

Graph of Force and Acceleration vs. Time

The maximum force exerted on the bungee jumper at any given time is 6.035 N. According to Newton’s second law of motion (F=ma), the total force on an object divided by its acceleration will equal the mass of the object. The graph of F/a is a horizontal line.

Force multiplied by Time during the Elastic Stretch Period

The area under the curve during the elastic stretch period is equal to the force multiplied by time during that time frame. Total area = 1.801 N⋅s. Velocity change during this time period is -0.50 m/s. Trial 3 Position vs Time

The point where the elastic started slowing the jumper was (2.950 s, 1.75 m). The lowest point of the fall was (3.100 s, 1.36 m). The total distance the elastic stretched was 0.39 meters. The largest change in position and time was 2.18 m/s, and the smallest change was 0.11 m/s; these values indicate values for the velocity of the bungee jumper. Acceleration during Free Fall

The average acceleration during free fall was -4.10 m/s^2.

Velocity during Freefall

The linear equation representing the velocity of the jumper in free fall is v=-5.39t + 13.7. Acceleration during Elastic Stretch Period

The curve of the acceleration of when the elastic band started stretching to when the jumper reached the bottom of it’s fall. The relationship is described by a=136t -399.

Velocity during Elastic Stretch Period

The fitted curve of the velocity of when the elastic band started stretching to when the jumper reached the bottom of it’s fall. The relationship is described by v=21.5t - 67.2.

The initial drop creates a large dip in values, which shows the amount of force that was exerted on the jumper in that initial drop. The jumper was in free fall until the point of (3.050 s, 4.966 N). From there, the elastic band is stretched until the object reaches (3.100 s , -10.028 N), which is where the maximum force of 10.028 Newtons is exerted onto the jumper.

A linear line was fitted to this function, as the initial fall resembles a linear line. The problem is that there only seem to be two points in this region of the graph. The equation for this function is N=-300t + 920. This function gives us the relationship between how much the elastic band was stretched and the force exerted on the jumper.

Force during the Free Fall Period

Force during Elastic Stretch Period

The maximum force exerted on the jumper is 10.028N at 3.100 sec when the bungee jumper is at its lowest point. Force, Acceleration, and F/A Plotted

F/A during Elastic Stretch Period

The mean value while the elastic is being stretched is -0.27 N/(m/sec2 ). According to Newton’s second law of motion, F=ma, the Force divided by the acceleration will result in the mass of the object. In this case, the mean value is a negative value close to zero which reveals that the object has a small mass with very little air resistance. Force multiplied by Time during the Elastic Stretch Period

The area under the curve from 2.950s - 3.100 s is equivalent to the force multiplied by time during the same period. In this instance, the area is 1.019 N⋅s. The total velocity change during this time is 2.24 m/sec.

Conclusion The bungee jumper begins its drop with a free fall until it reaches the length of the elastic cord, then the cord begins to stretch and slow the descent of the bungee jumper. When the bungee reaches its lowest point it’s pulled back up by the cord and continues to drop and bounce until the object runs out of energy. Each of these oscillations exerts a force on the bungee jumper, pushing it downward or upward. The results of this lab had multiple sources of error due to lab constraints. The equipment used was not capable of factoring in air resistance which made it

difficult to ensure that the object only moved vertically up and down. The object was prone to slight horizontal swaying most likely due to the object hitting particles in the air which altered its direction. The sensors are unable to detect this horizontal motion. Another source was the stability of the experiment set up. The pole used to secure the bungee jumper, force sensor, and elastic cord shook from the force of the bungee jumper being dropped. This extra movement from an object that is not the focus of the experiment could have altered results. In order to eliminate these sources of error the experiment would have to be performed in a vacuum with a sturdy and fixed set up....