Abstract
This laboratory experiment mainly focused on two parts; motion in the absence of force and motion in the presence of force. The professor walked at a constant speed to represent the absence of force. While the cart and inclined dynamic track was used to observe the presence of a force, which was weight. Each data was recorded and tabulated for their respected part. There are four figures to represent the relationship between position and time and velocity and time. For part A, a directly proportional plot was expected for position versus time graph and a horizontal line with a slope of zero was expected for the velocity versus time graph. In motion in the absence of force, the position versus time graph showed a slope of 1.25 and the velocity versus time graph had a near zero slope of -0.015. The experimental results in the motion of presence force showed an exponential graph for the position versus time and a linear graph for the velocity versus time with a slope of 25.14. For the most part, the experimental results correlated with the theoretical expectations.
Introduction
The objective of this laboratory is to understand distance versus time graphs by investigating straight line motion with both velocity and acceleration. A straight line motion with constant velocity can be observed by measuring the average velocity of an individual walking at a constant pace. In comparison, the straight line motion with constant acceleration can be observed by an inclined dynamic track with a cart. The experimental results are presented in several graphs (position vs. time and velocity vs. time) and can be interpreted to achieve the desired goals.
The study of motion basically pertains to the relationship between the change in position and the change in time. The change in position is represented by the symbol Δx, which is the difference between the initial position and final position. This is defined as the displacement of an object.
- Δx = x – xₒ [1]
The change of position over a given time is known as the average velocity. Velocity is known as a vector quality which gives a magnitude and direction. Velocity is important for measuring how fast an object is moving at a given time. For example, an individual can measure how quickly he/she will arrive to New York from Pennsylvania if he/she leaves at 8:00am. Velocity can be graphed to show the direct proportionality between time and position. Time resides on the x-axis while position is on the y-axis, The equation is denoted as :
- v =Δx/Δt [2]
There are two types of velocity; average velocity and instantaneous velocity. Average velocity is simply the total distance over the total amount of time traveled. On the other hand, instantaneous velocity is the speed that the object is traveling at that specific time. Instantaneous velocity is seen on the odometers of cars, which reads the exact speed that the driver is going at that given moment.
Objects do not always move at a constant velocity. For example, when the light turns red, a car must stop or when the car enters the expressway, it speeds up. Acceleration is useful to figure out how. The acceleration, denoted as a, refers to the change in velocity over a given period of time.
- a =Δv/Δt [3]
The main focus of this lab is to observe the motion with force and without force in different circumstances. If the motion is going at a constant velocity, then there is no force involved. However, if there is force involved then the motion shows a constant acceleration/
This laboratory is split into two parts. Part A deals with motion in the absence of force. The class will study the motion of the professor as he walks at a constant pace across 20 meters. The 20 meters are divided by blue tape at every 2 meter mark. Two people stand at each 2 meter mark with a stopwatch in their hands. As soon as the professor claps his hands, everyone must press the start button. Everytime the professor passes a blue tape mark, the two people standing at that marker must stop their stopwatch and record their position (meters) and time (seconds) on the board. Every lab group needs to set up columns on excel for time, position, velocity, acceleration, and time. The velocity and acceleration can be calculated from the position and time data. A velocity vs. time graph and position vs time graph must be made on excel using scatterplot. The R² value, trendline and equation of plot should be included on each graph.
Part B of the lab involves the motion in the presence of force by using an inclined dynamic track and a cart. Photogate 1 has to be connected to channel 1 of the smart timer and photogate 2, to channel 2 of the same timer. The photobeam of the photogate should be at the same level of the 2.5 cm flag. Start the smart timer and adjust some of the settings so the timer is ready to record. Photogate 1 must remain positioned at 20cm. However, after each trial, photogate 2 gets moved to different distances (x1 =30cm, x2 =40cm, x3 = 50 cm, etc). Release the cart from rest and a number should appear on the smart timer.
This is the time recorded between the two photogates. Record the distance (m) and time (s) on excel. Then, repeat the same procedure eight times for eight different x values and record their corresponding times. Make a position versus time graph, add a trendline and display the equation of each graph. Next, disconnect photogate 1, and set the smart timer to record velocity. Release the cart 7 times for 7 different positions (x1 =30cm, x2 =40cm, x3 = 50 cm, etc) and record the data on excel. Find the average acceleration and tabulate the results. Make a velocity versus time graph including the equation of the plot, the R² value and trendline.
There does not seem to be any significant errors in the position versus time graph. For the most part, all the points on the graph are near the slope line. Also, the slope is almost equal to zero. If there were any errors, it was probably due to certain lab groups lagging to stop their watches or the watches themselves are slower to stop. However, the velocity versus time graph does show errors. First of all, the slope should equal zero because there was an absence of force, which means the acceleration equals 0. The graph shows a slightly negative slope. A negative slope can be due to a few sources of error. Like mentioned before, these inconsistencies are most likely due to human error. Certain lab groups might have stopped their watches before the professor reached their mark and certain lab groups might have stopped their watches after the professor reached their mark.
Discussion
In Part A, the motion in the absence of force was shown by the professor walking a constant pace across 20 meters while each lab group stood 2 meters apart. Each group stopped their watches as soon as the professor reached their marker The data was recorded and tabulated in table 1. Based on theory, without force, an object should move at a constant velocity. Therefore, the acceleration should equal zero. It is hypothesized that graphing position versus time on the same graph will yield a linear plot and graphing velocity versus time will yield a horizontal line with a slope of zero. Figure 1 shows a positive linear slope of 1.248, which means that position is directly proportional to time. In figure 2, there should be a horizontal line with a slope of zero because the professor walked in a uniform pace with the absence of any force. The graph shows a slightly negative slope of -0.0514. The data is not correlating with the expected due to human error and the lack of accuracy of each stopwatch. One way we can solve this error is by taking out human error and using the same kind of timers that stop as soon as they sense motion, similar to the photogates.
In part B of the laboratory, the motion in the presence of force was observed. This involved the motion of a cart down an inclined dynamic track. The cart’s weight was the acting force. All the collected data from this part was recorded and tabulated in graph 2. According to theory, an object’s motion in the presence of force will show a constant acceleration. It can be hypothesized that the position versus time graph will be exponential and the velocity versus time will be linear. This is proven in figure 3, where the position is directly proportional to time squared. This shows that the acceleration of the cart was constant throughout the lab experiment. Figure 4 shows a positive linear slope, which proves that velocity is directly proportional to time.
Conclusion
All in all, the objectives of this laboratory were met. The motion in the absence of force was observed by having the professor walk 20 meters in a constant pace with each lab group timing how long it would take the professor to reach their mark. There were some small errors in this part of the experiment. It was expected that the velocity versus time graph would have a zero slope. However, the graph showed a slightly negative slope. This problem could be fixed if photogates were used instead of humans controlling a stopwatch. Also, there will always be a degree of human error when humans are conducting an experiment. The linear position versus time graph met expectations of constant velocity. As for observing the motion in the presence of a force, figure 3 showed an exponential relationship between position and time and figure 4 showed a linear relationship between velocity and time. Therefore, both figures represented constant acceleration.
