Florida Institute of Technology
© 2020 by J. Gering
Experiment 6
Newtons’ Second Law
Questions
What must be true in Newton’s Second Law (N2) if the object in question moves at a constant
velocity? Similarly, what must be true in N2 if the object accelerates? What are the customary
rules for drawing a Free Body Diagram (FBD)? What is the value of drawing an FBD? If two
objects are in contact with each other, what does Newton’s Third Law (N3) dictate should be
evident when FBDs are drawn of the two objects?
Concepts
Newton’s First Law is the also known as the law of inertia: an object at rest tends to stay at rest
and an object in motion tends to stay in motion. The second half really only applies to the
special case of straight line, constant velocity motion. One example is the motion of a ball
thrown from one astronaut to another inside a space station.
Newton’s Second Law (N2) is a statement of cause and effect. It states any object will undergo
an acceleration that is proportional to the vector sum of all the forces that act on the object. As
with all physical laws, this relationship is an experimental (empirical) result.
!
!
(1)
∑ Fi = ma
N2 places acceleration (change in velocity) at the center of the analysis. In contrast, Aristotle’s
teachings held that any motion implies a force acting on the object. Certainly, it requires a strong
push to start a stalled car moving and to keep it moving. But friction (another force) makes the
continued pushing necessary. In the absence of friction, when the initial push ends, the idealized
car would continue to move at constant speed in a straight line.
Do not treat mass multiplied by acceleration as if it were a force. Mass multiplied by
acceleration is the effect not the cause. The net force (always, initially on the left side of the
equation) is the WHY the object moves. Mass multiplied by acceleration is HOW the object
moves. Consequently, forces have the units of Newtons. Mass multiplied by acceleration has
equivalent units: kg m/s2 but we never call the units of mass multiplied by acceleration a
Newton. In physics, equivalence is different from being the same thing.
Method
In this experiment, students use an Atwood’s machine to accelerate two different hanging
masses. See Fig. 1. Here, two different masses hang from two pulleys, see Fig. 1.
6 – 1
Florida Institute of Technology
© 2020 by J. Gering
m
M
Figure 1. The Atwood’s Machine
A photo-gate is mounted around one pulley (not shown). It is used to measure the motion of the
pulley’s spokes. The data acquisition software then calculates the acceleration of the string and
hence the masses. We will assume massless and frictionless pulleys. Newton’s Second Law
predicts
⎛ M −m ⎞⎟
⎟g
(3)
a = ⎜⎜
⎜⎝ M + m ⎟⎟⎠
This equation can be derived in class. To do so, one draws free body diagrams of each mass and
applies N2. The key is to choose a direction for positive motion and then apply it throughout the
derivation. For example, if up is chosen to be positive, then the block of mass M in Fig. 1 will
have a negative acceleration. So, a minus sign must be placed in front of the ma term in N2 for
the more massive weight.
Procedure
1)
Arrange the apparatus so the heavy table clamp is near the edge of the table. Screw a
threaded rod into each pulley. In one case, use the threaded rod to also mount a
photogate around the pulley. Clamp both pulleys to the cross bar so a string passing over
them will move free and clear of the edge of the table.
2)
To set up the software, click on the Experiment menu and then click on the command Set
Up Sensors > Show All Interfaces. An image of the LabPro should appear with a photogate visible as the sensor. Click on the image of the photo-gate and a pop-up menu
should appear. Click on the Set Distance or Length… command. This will bring up
another selection menu. Choose the option labeled Ultra Pulley (10 Spoke) In Groove.
a) Use a total collection time more than the time it takes for the weight hanger to fall.
This way you will not be rushed to complete a run.
b) Set the data rate to at least 100 points per second. Place a foam pad beneath the
hanger you plan to allow to descend.
6 – 2
Florida Institute of Technology
© 2020 by J. Gering
c) Steady the weight hangers before each run to minimize swinging. Check the
alignment of the pulleys to reduce friction.
d) If the pulleys rotate when the mass hangers are empty, place paper clips or part of a
paper clip on one of the hangers to balance the hangers. Also use this method to
determine how much mass it takes to overcome the friction (and rotational inertia) of
the pulleys. Measure and record the small added mass. What type of error does this
procedure quantify?
e) Measure the mass of each weight hanger (and any object used to balance the
Atwood’s machine on a triple beam balance.
3)
Make one of the hanging masses 10 to 20 grams greater than the other. Using Logger
Pro, press the green collect button and then release the masses. Make sure the hanging
masses fall vertically and do not swing from side to side. Also make sure the string rides
in the pulley groove and does not slip out of the groove.
4)
Examine the distance, velocity and acceleration graphs. Use the Tangent command in the
Analyze menu (or on the ribbon) so a short line runs over the velocity graph. Measure
and record the slope of this tangent line at five different locations along that part of the
velocity graph that corresponds to a constant acceleration. Calculate an average of the
five slopes and a sample standard deviation. Record the average and a standard
deviation.
5)
Perform two more trials to ensure repeatability. Use different masses and different mass
differences.
6)
Write the name of everyone in the group, the section number and today’s date on the
graph using the Text Annotation command in the Insert menu. Create a screen capture of
one of your trials and email it to yourself. Include the image in your lab report.
For the Lab Report
1)
Compute the percent error in this ‘experimental’ acceleration.
2)
Compare your experimental and theoretical values by calculating a percent difference
between them. Is this percent difference smaller that the percent error you found above?
If so, the two accelerations agree within the limits of random error. Which type of
random error is largest here: error in measurement or intrinsic random error in the
acceleration? Is a systematic error present? What physical effect(s) cause(s) these
sources of error?
3)
For 5 points of extra credit, derive Equation (3) from Newton’s Second Law. For credit
to be awarded this work must be written by hand, not typed.
6 – 3
Florida Institute of Technology
© 2020 by J. Gering
This page has been left blank intentionally.
6 – 4
Experiment 06
Newton’s Second Law
Changes to the Procedures:
In-person students perform the experiment as written in the manual with one change. Instead
of using the Statistics command to average a fairly noisy acceleration vs. time graph, students
should use the Tangent command and record the slope of five tangent lines along each velocity
vs. time graph. Then, students can average those “velocity slopes” (as the software labels them)
to obtain the experimental value for the Atwood’s Machine’s acceleration. The standard
deviation of these five slopes provides the uncertainty in that average value for that one run.
There are no changes to the procedure for this experiment for at-a-distance instruction.
Data:
The data sets for at-a-distance students are distributed through a zero-credit quiz found in
Canvas > Quizzes > 06 Newtons Law Data.
2/28/22, 11:26 PM
Quiz: 06 Data
06 Data
Started: Feb 28 at 11:23pm
Quiz Instructions
This zero credit quiz is just a way to distribute different sets of data to students for the Newton’s Second
Law experiment. Students “take” the quiz and then copy and paste the data sets into their spreadsheet
for analysis.
Trial 8
Variable
Units
Value
Error
Description
m
g
111.00
0.100
mass on left
m2
g
111.30
0.100
mass on right
dm
g
40.00
0.100
mass added to
M = m2 + dm
g
151.30
g
m/s2
9.792
1
“velocity slope”
m/s2
1.400
2
“velocity slope”
m/s3
1.526
3
“velocity slope”
m/s4
1.530
4
“velocity slope”
m/s5
1.480
5
“velocity slope”
m/s6
1.573
Trial 1
Variable
Units
Value
Error
Description
m
g
51.50
0.100
mass on left
m2
g
51.20
0.100
mass on right
dm
g
10.00
0.100
mass added to
M = m2 + dm
g
61.20
g
m/s2
9.792
1
“velocity slope”
m/s2
0.812
2
“velocity slope”
m/s3
0.749
3
“velocity slope”
m/s4
0.808
https://fit.instructure.com/courses/596080/quizzes/941063/take
larger mass tha
0.005
larger mass tha
0.005
1/2
2/28/22, 11:26 PM
Quiz: 06 Data
4
“velocity slope”
m/s5
0.712
5
“velocity slope”
m/s6
0.875
Trial 3
Variable
Units
Value
Error
Description
m
g
71.50
0.100
mass on left
m2
g
71.20
0.100
mass on right
dm
g
15.00
0.100
mass added to
M = m2 + dm
g
86.20
g
m/s2
9.792
1
“velocity slope”
m/s2
0.809
2
“velocity slope”
m/s3
0.927
3
“velocity slope”
m/s4
0.962
4
“velocity slope”
m/s5
0.949
larger mass tha
0.005
No new data to save. Last checked at 11:25pm
https://fit.instructure.com/courses/596080/quizzes/941063/take
Submit Quiz
2/2
Course PHY 2091
EXPERMENT 5
Ahmed Muidh .A. Alotaibi
The date the experiment 11 June 20
The date the report 15 June 20
Instructor s name/ Casey
Introduction
In this lab students are going to perform an experiment in which two masses are attached on the
wheals with thread. So we will make first mass is greater in size with 10 to 20 gram so the
difference can make the system to move in one direction with overcoming the friction. Once the
system is in the required form so the greater mass will achieve an acceleration which will we
calculate here in this lab. We will use the equations mentioned in the lab manual and will find out
the changing velocity of the M by following Newton’s second law. Then we will plot these values
on graph and will try to verify them using the manual calculations so we can see that how much
we are accurately close to our final results and how much is our answer is deviating from the final
results.
Data
Trial 6: ZW
Variables
Units
Value
Error
m
g
81. 60
0. 050
M
g
101. 60
0. 050
g
ms-2
9.79 2
0. 005
aexp
ms-2
1.03 5
0. 098
Data analysis:
We will calculate the acceleration value by using the formula mentioned in the lab manual and
will verify the result which we have measured with the software.
?=(
?−?
)?
?+?
101.60 − 81.60
) (9.792)
?=(
101.60 + 81.60
? = ?. ??? ??−?
Error Calculation
Since we have calculated the value of acceleration and came to know that experimental value is
different from calculated values, so we will now calculate the percentage error occurring in the
value of acceleration.
% . ????? =
[???????? ?????] − ?[??????????? ?????]
. (100 )
[???????? ?????]
%????? ?? ? =
01 .035 − 1.068
∗ 100
1.035
%????? ?? ? = 3%
Data analysis says that we have 9.8% limit but our error is about 3% which means our results are
quite near to simulation or expected results. So in last we can say that our experiment is correctly
performed and we have achieved our lab goals.
Graph:
Figure 1
The graph is figure 1 have three plots red one is for the first mass centered graph is for the second
mass and the green one is for the acceleration. As we have talked that if the mass 1 has greater
value than mass 2 then it will have negative acceleration which can be seen by the green curve.
Discussion:
The results presented in the data analysis section depicts that the measure acceleration from the
software has approximately the same value like the calculated ones which means our performed
experiment have accurate readings. We have talked that our error should be minimized and we
have the minimum error which is 3% due to the machine error. There is no error present which
can disturb our value, and the graph in figure 1 is also showing the described behavior in order to
verify the final results.
Q1: What must be true in Newton’s Second Law (N2) if the object in question moves at a
constant velocity?
A.N: if the object has constant velocity so, change in velocity will give us [0] . As we know
accelertion is time rate of change in the velocity. If change in velocity will be [ 0 ], then acceleration
will be zero. So Newton second law force will also be zero.
F = ma = m(0) = 0
Q2: Similarly, what must be true in N2 if the object accelerates?
A.N: if an object is accelearting which means it has variation in velocity or we can say its change
of velocity is not zero, because there is some force acting on it according to the Newton’s second
law.
Q3: What are the customary rules for drawing a Free Body Diagram (FBD)?
A.N:. The only way for design freebody dia-grams is to depict
forcess that exist for object in the specific situation. There no
fast way about number of forces that must be drawn in a freebody
diagram..
Q4: What is the value of drawing an FBD?
A.N: We take the reference point from our side and draw the unit vector in length to draw the force
in all directions. We have shown that there are 4 types of forces in the FBD which will draw like
that.
Q5: If two objects are in contact with each other, what does Newton’s Third Law (N3) dictate
should be evident when FBDs are drawn of the two objects?
A.N: Newton 3rd law describes that every force has the same reaction force in the opposite
direction with same magnitude. So we are going to draw a FBD diagram for the two objects then
we have to keep this rule in mind for the sake of accuracy.
Conclusion
In this lab we have seen that how the acceleration of the mass can be calculated by using the
newton’s second law. This has done by an arrangement of hanging masses system as shown in the
manual and first mass is different than the second one so in this way the change in velocity has
happened and the acceleration has produced. This acceleration is negative if we take the up
direction and positive if we will take down. We have also plotted the graph in figure 1 to show the
negative acceleration and we have explained why this is happening so. In last we will summarize
the concept that the forces are computed by using newton’s second law if it has changing velocity.
Extra credit
Course PHY 2091
EXPERMENT 5
Introduction
In this lab students are going to perform an experiment in which two masses are attached on the
wheals with thread. So we will make first mass is greater in size with 10 to 20 gram so the
difference can make the system to move in one direction with overcoming the friction. Once the
system is in the required form so the greater mass will achieve an acceleration which will we
calculate here in this lab. We will use the equations mentioned in the lab manual and will find out
the changing velocity of the M by following Newton’s second law. Then we will plot these values
on graph and will try to verify them using the manual calculations so we can see that how much
we are accurately close to our final results and how much is our answer is deviating from the final
results.
Data
Trial 6: ZW
Variables
Units
Value
Error
m
g
81. 60
0. 050
M
g
101. 60
0. 050
g
ms-2
9.79 2
0. 005
aexp
ms-2
1.03 5
0. 098
Data analysis:
We will calculate the acceleration value by using the formula mentioned in the lab manual and
will verify the result which we have measured with the software.
?=(
?−?
)?
?+?
101.60 − 81.60
) (9.792)
?=(
101.60 + 81.60
? = ?. ??? ??−?
Error Calculation
Since we have calculated the value of acceleration and came to know that experimental value is
different from calculated values, so we will now calculate the percentage error occurring in the
value of acceleration.
% . ????? =
[???????? ?????] − ?[??????????? ?????]
. (100 )
[???????? ?????]
%????? ?? ? =
01 .035 − 1.068
∗ 100
1.035
%????? ?? ? = 3%
Data analysis says that we have 9.8% limit but our error is about 3% which means our results are
quite near to simulation or expected results. So in last we can say that our experiment is correctly
performed and we have achieved our lab goals.
Graph:
Figure 1
The graph is figure 1 have three plots red one is for the first mass centered graph is for the second
mass and the green one is for the acceleration. As we have talked that if the mass 1 has greater
value than mass 2 then it will have negative acceleration which can be seen by the green curve.
Discussion:
The results presented in the data analysis section depicts that the measure acceleration from the
software has approximately the same value like the calculated ones which means our performed
experiment have accurate readings. We have talked that our error should be minimized and we
have the minimum error which is 3% due to the machine error. There is no error present which
can disturb our value, and the graph in figure 1 is also showing the described behavior in order to
verify the final results.
Q1: What must be true in Newton’s Second Law (N2) if the object in question moves at a
constant velocity?
A.N: if the object has constant velocity so, change in velocity will give us [0] . As we know
accelertion is time rate of change in the velocity. If change in velocity will be [ 0 ], then acceleration
will be zero. So Newton second law force will also be zero.
F = ma = m(0) = 0
Q2: Similarly, what must be true in N2 if the object accelerates?
A.N: if an object is accelearting which means it has variation in velocity or we can say its change
of velocity is not zero, because there is some force acting on it according to the Newton’s second
law.
Q3: What are the customary rules for drawing a Free Body Diagram (FBD)?
A.N:. The only way for design freebody dia-grams is to depict
forcess that exist for object in the specific situation. There no
fast way about number of forces that must be drawn in a freebody
diagram..
Q4: What is the value of drawing an FBD?
A.N: We take the reference point from our side and draw the unit vector in length to draw the force
in all directions. We have shown that there are 4 types of forces in the FBD which will draw like
that.
Q5: If two objects are in contact with each other, what does Newton’s Third Law (N3) dictate
should be evident when FBDs are drawn of the two objects?
A.N: Newton 3rd law describes that every force has the same reaction force in the opposite
direction with same magnitude. So we are going to draw a FBD diagram for the two objects then
we have to keep this rule in mind for the sake of accuracy.
Conclusion
In this lab we have seen that how the acceleration of the mass can be calculated by using the
newton’s second law. This has done by an arrangement of hanging masses system as shown in the
manual and first mass is different than the second one so in this way the change in velocity has
happened and the acceleration has produced. This acceleration is negative if we take the up
direction and positive if we will take down. We have also plotted the graph in figure 1 to show the
negative acceleration and we have explained why this is happening so. In last we will summarize
the concept that the forces are computed by using newton’s second law if it has changing velocity.
Extra credit
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