Labreport 1 - Experiment #2: One Dimensional Motion with Constant Acceleration PDF

Preview

Summary

Experiment #2: One Dimensional Motion with Constant Acceleration...

Description

Courtney Grigsby PLAB 193-07 Dr. Patrick Moyer 9 Oct 2019

Experiment #2: One Dimensional Motion with Constant Acceleration

Objective: The goal of this lab is to understand the relationship between position, time, velocity, and acceleration. Specifically, investigating these factors as an object moves in one dimension along a straight line. Additionally, we will visualize this relationship by graphically analyzing the motion of objects. Background: Speed is a measurement of how fast an object moves relative to a reference point. It does not have a direction. Speed can be figured by the formula:

s=

d t

Where speed(s) equals distance(d) divided by time(t). Velocity is the rate of change in an object's position over time. Velocity has a magnitude (speed) and a direction. The formula for velocity is:

v =

( x f −x i ) Δ x ∨v = Δt t −t ( f i)

Where velocity, (  V ) equals the change in position ( Δ x ) divided by the change in time ( Δt ). Acceleration is the rate of change of an object’s velocity with time. Acceleration not only has a magnitude, but also has a direction. This makes acceleration a vector.

Acceleration can be found using the formula:

a=

Δv Δt

Where acceleration equal the change in velocity divided by the change in time. When you accelerate or decelerate, you change your velocity by a specific amount over a specific amount of time. Experimental Procedure: A graph was constructed using the data of runners 1, 3, and 5. The data contained the times at which it took each runner to reach a specific distance. Distance, measured in meters, was plotted along the vertical (y-axis), and time, measured in seconds, was plotted along the horizontal axis (x-axis). Each runners’ was assigned a unique color, in which their data points were plotted in. This was done to distinctly identify what data belong to what runner, and avoid confusion. After all available data was put into the graph a “best-fit” curve was assigned to each runners based on the points plotted. Data: Please see attachments for data and graph.

Runner #5 instantaneous velocity: (4.5, 36), (7.5, 74) 2

Δ x  V= Δt

v=

74−36 7.5 −4.5

v(instantaneous) ≈ 12.67 m/s Runner #5 speed in miles per hour: 1 2∈¿ 1 ft ¿ ¿ 1 m ∈¿ 60 s ¿ ¿ 1∈ ¿ ¿ 2.54 cm 12.67 m 100 cm ¿ 1s 1m

(

)

= 28.34 mph Discussion: The slope of the “best fit” curve” found for an object represents the velocity of the object. Therefore, the value of the slope at a particular time represents the velocity of the object at that instant. Viewing the information graphically allowed us to make general observations about the data. For example runner #5 was the fastest of the group, while runner #3 was the slowest. Additionally, runner #5 appeared to have the steepest slope of the group. Implying runner #5’s speed was increasing at a faster rate than that of others. We were

3

also able to notice all the runner’s “best fit” lines assigned were curved, indicating a change in the runners accelerations. Which is best represented with the equation of

constant acceleration:

1 2 x = x 0 + v 0 t+ at 2

Further calculations were only preformed on data associated with runner #5. The runner’s instantaneous velocity of approximately 12.67 m/s at 7.5 s was determined using the two points (4.5, 36) and (7.5 , 74), obtained from the runner’s “best fit” curve. The runner’s speed was determined by converting the instantaneous velocity of 12.67 m/s to 28.34 m/h . Conclusion: This experiment was preformed to study the connection between position, velocity and how they relate to the acceleration of an object. Specifically, this demonstration focused on objects moving in one dimension, along a straight line. Using data of the three runners, we were able to construct a graph to visualize the runners’ positions in time. This demonstrated how position and time relate to each other. Assigning a “best fit” curve” to the runners’ data points gave us a better understanding of the runner’s motion, and how it changed. Furthermore, it also aided in exxplaining the relationship between position, velocity, and acceleration. As a heavy equipment operator in the Louisiana Army National Guard, we often must drive large vehicles wherever they are needed. The application of this lab can be seen in the operation of those vehicles. For example, in determining the maximum speed a 20 -ton dump truck can achieve with a full load of material; additionally, how long it 4

will take for the truck to reach that speed. This is useful in accurately estimating the time and resources needed to complete a mission.

5...