Question

Physics 100 – Uniform Motion Page 1 of 6
SAN DIEGO MESA COLLEGE Name_________________________
PHYSICS 100 LAB REPORT Date __________Time___________
Partners ______________________
TITLE: Uniform Motion ______________________________
______________________________
______________________________
Objective: To determine the equation of motion for a toy tractor.
Theory: The motion of an object is described by the change of it's position with respect to time,
as measured from a start point for it's position and it's time ( i.e. at x=0 and t=0). The
mathematical relationship for an object's position as a function of the time it reaches
that position is called the object's equation of motion. The simplest equation of motion
is for motion without acceleration. This motion is called uniform motion.
Equipment: motorized cart tape timer mount
tape-timers 1 1/2 meter strips
meter-stick brick
masking tape
Setup:
Paper strip 1.5 meters long
Masking tape
Brick
C(caarbrboonn p saidpe ru dpi s)k
Tapper
M o ctaortiz ed
Physics 100 – Uniform Motion Page 2 of 6
Technique: The tape timer has a circular piece of carbon paper and a tapping mechanism. The
tapper taps on the carbon paper specific number of times per second. As the toy tractor
moves, the tape timer puts marks on the paper strip at regular time intervals. The
amount of time between marks (the Δt) is decided by which direction the switch on the
timer is moved when it is turned on. There are two settings 10Hz and 40Hz. We will be
using the 10Hz setting for a Δt = 0.1seconds. The tractor will move a certain distance
Δx between each mark. These two sets of values will give us the data we need to get
the equation of motion.
Procedure: Turn the tractor on temporarily to see which direction it will move.
Face it so it will move away from the tape timer.
Get one of the long paper strips.
Feed one end through the first plastic slot, then in between the silver metal plate and the
circular piece of carbon paper, and out through the other plastic slot. If it's not feeding
easily, slightly bend a small portion of the end of the paper strip. This might help.
Take a small piece of masking tape and tape the end of the paper strip nearest to the
timer to the top of the tractor.
Place the tractor near the tape timer, but leave enough room to lift the tractor off the
table a little bit (you'll lift it later).
Pull the rest of the tape out the back of the tape timer so that it is hanging over the edge
of the table.
Have one partner lift the tractor off the table enough so that they can turn the tractor on.
Have another partner on the opposite end of the table ready to stop the tractor.
Have a third partner move the switch on the tape timer to the 10Hz position. The timer
should start clicking.
Have the person with the tractor turn it on, aim it towards the brick and set it on the
table.
Once the tractor gets to the other side of the table, move the timer's switch to the off
position to turn it off.
Remove the paper strip from the tractor and turn it over. Make sure the marks made by
the timer are dark and visible.
If they are easily visible, then you are ready to start the analysis. If not, try rotating the
circular piece of carbon paper and run through the procedure again. If this still doesn't
produce visible marks, ask the instructor for help.
Analysis: Look at the marks (dots) on your strip.
The beginning of your strip is the side that was attached to the tractor. The first few
marks probably won't look evenly spaced.
Choose and circle the first dot, after skipping several, which appears sharp and is
evenly spaced with its neighbors. This is dot #1 which occurs at t = 0 sec. and has a
starting position of x = 0 cm.
Lay the paper strip along a meter stick or ruler and use masking tape to attach the first
dot you choose for t = 0 and x= 0 to the zero end of your meter stick or ruler.
Physics 100 – Uniform Motion Page 3 of 6
Record the position of where each dot is along the ruler or meter stick.
Calculate the distance interval between each dot and the dot before it. The distance
interval is the position of each dot minus the position of the dot before it. The distance
interval is also known as Δx.
Dot # Position
(cm)
Time
(Ticks)
Distance
Interval
(cm)
Ave.Velocity
In interval
1 0.0 0 (cm/sec)
2 1
3 2
4 3
5 4
6 5
7 6
8 7
9 8
10 9
The average velocity that the object obtains during an interval of one tick is the distance
interval traveled during that one tick divided by the time elapsed (one tick). To
calculate the average velocity, divide the distance interval by one tick.
This gives you units of cm / tick.
To convert this to a usable number, you will need to multiply this number by the
Number of ticks per 1 second.
There are 10 ticks per second.
This will give you units of cm / sec.
Fill in your table with each of the average velocities.
Physics 100 – Uniform Motion Page 4 of 6
Because the motion is uniform, the average velocity over all the intervals can be found
by adding up all the average velocities, and dividing by the total number of average
velocities intervals.
Record this value below the average velocity column on the data sheet.
Analysis: The equation of motion is found by plotting the distance (in cm, on the y-axis) as a
function of time (in ticks, on the x-axis).
Plot this on the linear graph paper provided in your lab packet.
Calculate the slope of your graph, showing all work including units, in the space
provided below.
(Dfinal - Dinitial) / (Tfinal - Tinitial) = slope
Where D is distance in cm and T is the time in ticks
Convert this slope to cm / second using the same conversion as you did for the average
velocity.
SLOPE FROM GRAPH: CONVERSION:
Calculate the percent difference, in the space provided below, between the average
velocity from the data sheet and the slope of the graph, using the formula:
% difference = (difference between two experimental values / the larger of two values)
x 100
What name is given to the constant (the slope of the graph) which relates the distance
traveled by the tractor and the time it took to get to that distance?
Physics 100 – Uniform Motion Page 5 of 6
Write the equation of the graph, in the form y = mx + b. in the space below. Where y is
the variable plotted on the vertical axis and x is the variable plotted on the
horizontal axis, m is the slope of the graph, and b is the vertical intercept. The vertical
intercept, b, will be close enough to zero to be neglected.
Don't forget to include units in your equation.
Use this equation to calculate, showing all work including units in the space provided
below, how far the tractor would travel in 45 seconds.
How many meters is this? Show your work in converting the units.
How many yards is this? Show your work in converting the units.
Analysis:
Use this equation of motion to predict how many MINUTES it would take the tractor to
Travel 11.78m which is the length of the lab room.
Show all your work below including unit conversions.
Physics 100 – Uniform Motion Page 6 of 6
Summary of Results:(What is the equation of motion for the tractor, in words)?

Answer 1

Ave.Velocity
In interval (cm/s)

1 0

2 1
3 2
4 3
5 4
6 5
7 6
8 7
9 8
10 9

The average velocity = (10+21+32+43+54+65+76+87+98+109) / 10

The average velocity = 595/10 = 59.5 cm/tick

Unit convertion from cm/tick to cm/s, nothing but multiply by 10

The average velocity = 595 cm/s = 5.95 m/s

% difference = (difference between two experimental values / the larger of two values) x 100

% difference = [ (21-10)/21 ]100 = 52.381

% difference = [(32-21)/32]100 = 34.375

% difference = [(43-32)/43]100 = 25.581

% difference = (11/54)100 = 20.37

% difference = (11/65)100 = 16.923

% difference = (11/76)100 = 14.474

% difference = (11/87)100 = 12.643

% difference = (11/98)100 = 11.224

% difference = (11/109)100 = 10.092

Distance covered in 45 seconds is

Distance = speed / time = 595 / 45 = 13.22 cm = 0.1322 m

Convert Meter in to yards [ 1 m = 1.09361 Yard ], Therefore

Distance = 0.1322 m = 0.1445 yards

Time = Speed / distance = 5.95 / 11.78 = 0.5051 s

For an uniform motion, equation of motion is

v = u + at

s = ut + (1/2)at²

v² = u² + 2as

u - Initial velocity of the tractor

v - Final velocity of the tractor

a - Acceleration of the tractor

s - Displacement of the tractor with respect to time