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i need help for this lab , i have attached the data and the manual please follow the manual , thanks
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Florida Institute of Technology
© 2023 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.
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Florida Institute of Technology
© 2023 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)
Set up the software.
a) Click on Experiment > Set Up Sensors > Show All Interfaces. An image of the
LabPro should appear with a photo-gate visible as the sensor. Click on the image of
the photo-gate and a pop-up menu should appear.
i) Select Motion Timing.
ii) Also select Set Distance or Length… , then choose Ultra Pulley (10 Spoke) In
Groove.
b) Execute the Experiment > Data Collection command.
6 – 2
Florida Institute of Technology
© 2023 by J. Gering
i) Set a total collection time of 10 seconds. This should ensure you will not be
rushed to complete a run.
ii) Also set the data rate to 100 points per second.
3)
Prepare for a run.
a) Place a foam pad beneath the hanger you plan to allow to descend.
b) Ensure the pulleys spin in the same plane and both pulleys are at the same height.
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 a 1 gram mass, a small
paper clip, or part of a paper clip on one of the hangers to achieve static equilibrium.
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.
4)
Make one of the hanging masses 10, 15, 20 or 25 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.
5)
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 seven different locations along that part of the
velocity graph that corresponds to a constant acceleration. Calculate an average of the
seven slopes and a sample standard deviation. Record the average and a standard
deviation.
6)
Using different masses and different mass differences, perform two more trials. If
working in a group of three, trade off the tasks of releasing the hangers and using the
software.
7)
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.
6 – 3
Florida Institute of Technology
© 2023 by J. Gering
For the Lab Report
1)
Compute the percent error in this ‘experimental’ acceleration.
2)
Derive Equation (3) from Newton’s Second Law. This work must be written by hand, not
typed.
3)
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?
6 – 4
hi
hi
hi
hi
hi
hi
Noah
Levent
Kelly
Abdullah A
Phy 2091
Trial
Mass Difference (g)Slopes
1 40 – 25 = 15
Avg Acceleration
0.693
St Dev
0.763
0.039450391
0.462571429
0.003952094
0.645428571
0.006900656
0.726
0.765
0.776
0.787
0.799
0.795
2 50 – 40 = 10
0.462
0.459
0.464
0.469
0.462
0.465
0.457
3 100 – 80 = 20
0.643
0.64
0.639
0.652
0.657
0.647
0.64
hi
Mass of Hanger
50.8 g
a Theo
2.2597
1.088
1.088
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