Phisycal Science
Paul Pog
Lab4.pdf
2nd Edition Introductory Physics Student Manual
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Safety Information
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Sample Labware
Lab 4 1-D Kinematics
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1-D Kinematics
Introduction
1-D kinematics occurs when an object travels in one dimension and
can be described using words, equations and graphs. Linear mo- tion describes how an object will move horizontally or vertically with constant acceleration, how an object will travel if dropped from the
side of a cliff, and the path it will follow if thrown straight up into the
air. Keep in mind the motion of an object is relative to the viewer.
Even though you do not feel like you are in motion right now, you are
on planet earth that has rotational motion in addition to orbital motion
around the sun. In almost all cases here motion will be relative to the
Earth.
Speed, Velocity and Acceleration You may be familiar with speed outside of the physics classroom. When you drive in a car you are traveling a distance over a certain amount of time: a speed. How then is velocity different from speed? Velocity (v) is a vector quantity described as the rate at which an object’s position changes divided by the time the object is
in motion. Furthermore, the rate of change in velocity plays an important role in physics. Acceleration repre- sents the rate of change of an object’s velocity over time.
In physics, quantities can be scalar or vector. The difference between the two lies in direction. Scalar quanti- ties include magnitudes, which are numerical measurements. The distance an object has traveled or the
speed of an object is a scalar quantity. Scalars do not take direction into consideration. Vector quantities in- clude magnitude and direction. The displacement from an object’s initial position, velocity and acceleration
are vector quantities. The direction of vectors can be described as being in the positive direction, in the nega-
tive direction, north, south, east, west, left, right, up, down, etc. It is important to distinguish between scalar
and vector quantities when trying to understand kinematics.
Learning Objectives
• Distinguish between scalar and vector quantities
• Apply kinematic equations to 1-D motion
• Interpret 1-D motion graphs
• Predict position, velocity, and acceleration vs. time graphs
• Calculate average and instantaneous velocity or acceleration
Figure 1: Pool balls in motion demon- strate 1-D kinematics.
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1-D Kinematics
Speed, velocity and acceleration can change during an object’s motion. An object’s speed, velocity or accel-
eration at any one point in time during its motion is referred to as instantaneous. The total change in an ob-
ject’s distance over time is referred to as average speed, the average change in an object’s position over time
is referred to average velocity and the average change in an object’s velocity over time is referred to as aver-
age acceleration.
Example 1: Speed A car travels a distance of 800 meters over a time of 10 seconds.
The car has an average speed of 80 meters per second (Figure
2).
Example 2: Velocity
A car travels at 800 meters west. The car makes a U-turn and trav-
els a distance of 800 meters east. It took the car 20 seconds to com-
plete its course. The average velocity of the car is 0 meters per se-
cond (Figure 3) because the car travels in opposite directions that
cancel each other out.
Even though the car experienced a lot of motion in 20 seconds its position did not change over the course of
its motion. Example 3: Acceleration
A car travels from 0 m/s to 90 m/s in 15 seconds.
The car has an average acceleration of 6 m/s2.
distance
time SpeedAVG =
800 m
10 s = =
80 m
s = 80 m/s
∆displacement
time VelocityAVG (vAVG) =
800 m + (-800) m
20 s = =
0 m
20 s = 0 m/s
Figure 3: Diagram showing the velocity of a car.
∆velocity AccelerationAVG (aAVG) =
time
90 m/s =
15 s =
6 m/s
s = 6 m/s2
Figure 2: Diagram showing the average speed of a car. Speed is scalar.
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1-D Kinematics
The Kinematic Equations Equations that relate the position, velocity, and acceleration of an object moving in a straight path are called
linear kinematic equations. These equations are used to solve for the instantaneous position, velocity, or ac-
celeration of an object. The three general equations of linear motion for an object with constant acceleration
are:
where:
df is the final position (m) d0 is the initial position (m) d is displacement which is equal to df - d0 t is the amount of time the object is in motion (s) vf is the final velocity (m/s) v0 is the initial velocity (m/s) a is acceleration (m/s2)
Many equations can be derived from the general equations to find the above variables under different condi-
tions as long as all variables except the one being solved for are known. Let’s take a look at some examples.
If the initial velocity of the object is equal to 0 m/s and initial position is equal to 0 m, the kinematic equations
simplify to:
vf = at
df = ½ at2
The following equation is useful to find the displacement an object travels when gravity is the only force acting
on the object and the time is known. The acceleration of gravity, g, on earth is about 9.8 m/s2:
d = ½ gt2 Acceleration and Gravity
Gravity causes objects to accelerate downward when falling. In reality, air resistance decreases the effects of gravity on the accelerating objects until it balances the force of gravity and there is no longer a change in ve-
locity – when the object reaches its terminal velocity (Figure 4). However, when we study linear motion, it is
convenient to neglect air resistance and focus only on the acceleration due to gravity (g), a state called free fall. In all cases of free fall, g (9.8 m/s2) is the acceleration due to the force of gravity that can act in a positive
df = d0 + v0t + ½ at2
vf = v0 + at
vf2 = v02 + 2ad
Relates distance and time
Relates velocity and time
Relates velocity and displacement
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1-D Kinematics
way by increasing the speed of the object or nega-
tively by decreasing the speed. Thus, for every
second of free fall there is a change in velocity of
approximately 10 m/s. This leads us to the equa-
tion for the acceleration of a falling object: vf = gt
where v is the final velocity (m/s), g is the acceler- ation due to gravity (9.8 m/s2), and t is the elapsed time (s). Thus, velocity is a function both of accel-
eration and of how long the object is acted on by
that force.
Gravity is also responsible for slowing down an
object thrown straight up into the air and accelerat-
ing it back to Earth. In fact, the object reaches a
point of zero velocity before it changes directions.
This characteristic behavior is typical of all mass in
the presence of gravity.
Graphing 1-D Motion
In science, we observe how one factor changes as a result of a change in another. The effect of one variable
on another can be expressed as a function. An alternative to using equations to describe motion is to utilize
motion graphs to visualize the same relationships.
When we look at the speed versus time graph of an object in free fall (Figure 5), we observe a linear relation-
Figure 4: Skydivers experience free-fall. To reduce the effects of air resistance, skydivers orient their bodies perpendicular to the ground. By doing this, they are able to reach a terminal velocity of about 120 mph!
? ? ? ? Did You Know... Did You Know... Did You Know... Did You Know... Physics is the study of how the world works. Cur- rently, all physics has been described by the interac- tion of particles in space at a certain time. We refer to this arena for particles to interact and collide with each other “space-time”. Recently, physicist a new kind of geometric shape called the amplituhedron was discovered to simplify calculations for colliding particles. Could this be the end of “space-time”?
Pictured to right: Amplituhedron
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1-D Kinematics ship. In other words, for every increase in time, there is the same increase in speed. Since the object is
dropped from rest, the line starts at the origin (0,0). Since this particular curve is a straight line, we know
the slope (∆y/ ∆x) of the line is constant. On this graph, the slope of the line represents acceleration. The
steeper the curve (the line) is, the greater the acceleration. From the data presented here we know that
the acceleration pictured in Figure 5 is constant.
Examining the curves on a velocity vs. time graph provides information about the direction, speed and
acceleration of the moving object. Take a look at the series of linear motion graphs in Figure 5 and how
they are interpreted.
Figure 5: Linear motion graphs.
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1-D Kinematics
Understanding the meaning of the shape and slope of a distance vs. time graph is essential to your under-
standing of linear motion. Whether it’s the speed or direction that is changing, the rate of acceleration will
greatly influence the path of motion. From driving your car to shooting a gun, these concepts apply to many
situations encountered in everyday life. Explore the world around you and see how many applications of line-
ar motion you can identify!
Pre-Lab Questions
1. What is the acceleration of a ball that is vertically tossed up when it reaches its maximum height?
2. If you drop a ball, and then one second later drop a ball identical in mass, size and shape, what happens
to the distance between them as they fall?
3. What does a positive and negative slope represent for a velocity versus time graph?
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1-D Kinematics
Experiment 1: Distance of Free Fall
In this experiment you will explore the time it takes for hex nuts at varying initial distances to hit the ground as
a result of free fall. Hex nuts will be tied to a string, which will provide audible data for the rate of free fall as
they hit a metal pan.
Procedure 1. Develop a hypothesis for testing the effect of varying distances on time for objects in free fall. What do
you predict will happen? Record your hypothesis in the Post Lab section in the answer space for Question
1.
2. Use the measuring tape and scissors to measure and cut 2.5 m of string.
3. Tie the hex nuts 40 cm apart along the length of the string, starting with one on the end. There may be
extra string on one end of the set up.
4. You will have to stand on something tall enough for the length of string to be suspended. Try a chair, a
ladder, or stairs with an open railing to one side. See Figure 6 for set up.
LAB SAFETY: Be careful that you are fully supported with whichever method you choose.
Materials
Catch Pan
6 Hex Nuts
Scissors
Stopwatch
2.5 m String
Tape Measure
*Something Tall to Stand On
*You Must Provide
A
B
Figure 6: Nut spacing for Experiment 1.
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1-D Kinematics
5. Hold the string over the pan so that the first hex nut is slightly above the metal surface. Let the hex nuts
come to as much of a rest as possible before dropping them.
6. Let go of the string and observe the resulting pattern of “clangs” as each hex nut hits. Do this several
times to get an idea for the pattern.
7. Keeping one hex nut on the end, change the spacing between each successive hex nut to follow the se-
ries: 9, 27, 45, 63, and 81 cm (Figure 5b). Drop the string several times to observe the new pattern.
8. Remove one hex nut from the string.
9. Use the tape measure to choose a distance no taller than the top of your head. Mark the height with a
piece of tape on a wall or stable, vertical surface. Record your drop height in Table 1.
10. Use the stopwatch to record how long it takes the hex nut to hit the metal pan in Table 1. Repeat two
more times, and find the average.
Data
Auditory Observations of Equally Spaced Hex Nut Pattern:
Auditory Observations of Unequally Spaced Hex Nut Pattern:
Table 1: Washer Free Fall Data
Trial Time (s)
1
2
3
Average
Drop Height (m)
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1-D Kinematics
Post-Lab Questions
1. Record your hypothesis from Step 1 here. Use evidence from your results to explain if your hypothesis
was supported or not.
2. What was the difference between the noise patterns for equally spaced hex nuts compared to the une-
qually spaced hex nuts?
3. What caused the differing noise patterns?
4. Define the independent and dependent variables in the experiment.
