Introductory and AP Physics Exercise 1: Introduction to Laboratory Techniques – Linear and Projectile Motion

Introductory and AP Physics Exercise 1: Introduction to Laboratory Techniques

Purpose

The purpose of laboratory exercise 1 is to test and verify Isaac Newton’s Second Law of Motion in relation to the motion of an object. This exercise aims to familiarize the experimenter with the basic presentation used in a Physics experiment, provide experience with graphing data, and introduce techniques for analyzing and presenting experimental data.

Method

In laboratory exercise 1, Introduction to Laboratory Techniques, proper methods of presenting a physics experiment were employed. This involved analyzing, interpreting, and recording data that describe variables related to the linear motion of an object, specifically velocity, distance, and time. The approach included tabulating data, applying proportionalities and their standard units, graphing data, and determining slopes in the graphs to understand their physical significance. Data tables were formatted with titles, explanations of experimental conditions, and assigned units and labels for columns of data.

Data

Example:

Table 1: Distance versus Time for a Car Moving at a Constant Speed of v = 5 m/s

t (sec) s (meters)
0 0
1 5
2 10
3 15
4 20
5 25

The above table illustrates one way to present the experiment’s data regarding tracking the car’s position. The corresponding graph is shown below.

Graph 1: Distance versus Time for a Car Moving at a Constant Speed of v = 5 m/s

The slope of the line in the graph represents the change in vertical distance over the change in horizontal time, determining the ratio units:

Change in Vertical = s = 25 – 5 = 20m Change in Horizontal = t = 5 – 1 = 4 seconds

Slope = 20m / 4 sec = 5 m/s

The slope of a linear graph corresponds to the proportionality constant observed in the table or equation representations. It carries physical meaning, and the units are determined by the function and variable.

Data Set 1: Distance Versus Time for a Car Moving in a Straight Line

A car is observed to be moving in a straight line, and the following positions are recorded at specific times:

Table 2: Distance Versus Time for a Car Moving in a Straight Line

t (sec) s (meters)
5 124
10 152
15 175
20 202
25 225
30 245
35 275
40 305

Graph 2: Distance Versus Time for a Car Moving in a Straight Line (Data Set 1)

The slope of the line in the graph, Distance Versus Time for a Moving Car (Data Set 1), can be calculated to determine the change in vertical distance over the change in horizontal time and find the ratio in m/s:

Change in Vertical = s = 305 – 124 = 181m Change in Horizontal = t = 40 – 5 = 35 seconds

Slope = 181m / 35 sec = 5.143 m/s

The slope represents the change in time proportional to the changes in distance at various time intervals. In this linear graph, the slope defines the proportionality constant observed in Data Set 1.

Data Set 2: Distance (Position) Versus Time for a Car Accelerating in a Straight Line Motion

A car is known to be accelerating in straight-line motion, and position and time data are recorded:

Table 3: Distance (Position) Versus Time for a Car Accelerating in a Straight Line Motion

t (sec) s (meters)
0 0
1 0.6
2 2
3 5
4 9
5 12
6 17
7 25
8 32
9 40
10 51

Graph 3: Position Versus Time for a Car Accelerating in a Straight Line Motion (Data Set 2)

The graph shows a curve representing the relationship between position and time, indicating non-linear motion.

The curve in the graph, Distance Versus Time for a Moving Car (Data Set 2), can be used to find the instantaneous velocity of the car at any time. In this exercise, the line was used to calculate the instantaneous velocity at t = 3, 5, 7, and 9 seconds. The resulting data is tabulated in the following table:

Table 4: Velocity Versus Time for a Car Accelerating in a Straight Line Motion

time (sec) Velocity (m/s)
3 3.5
5 1.25
7 0.5
9 0.125

The velocity at each time was estimated using the corresponding displacement values and time intervals.

Conclusion

The experiments conducted in laboratory exercise 1 aimed to test and verify Isaac Newton’s Second Law of Motion. The conclusion of the experiment successfully met the objective by exploring the physical significance of position versus time and velocity versus time. The experiment involved tabulating data, graphing position and velocity, and applying concepts of Kinematics.

Position versus time data was used to illustrate the displacement of an object at different times, allowing estimation of velocity or the rate of change of position. Velocity versus time graphs enabled the calculation of slopes to determine acceleration and average acceleration over time. Curved slopes indicated changes in acceleration over time.

The exercise also achieved its objective of familiarizing the experimenter with the basic presentation and analysis methods used in Physics experiments. Graphing techniques, including the use of programs like Microsoft Excel, were introduced, and the determination of slopes and their physical significance was demonstrated. Overall, the objectives and purposes of the exercises were successfully accomplished.