LAB 3
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Masrurah Morshed
10/1/2023
PHY 133
TA: Zijian Zhou
Force and Friction
Introduction
In this experiment, we investigate the force of friction and how it varies when we add weight. Friction is like a speed bump for moving objects, and it comes in two varieties: static, which prevents things from moving in the first place, and kinetic, which slows things down after they're going.
Our purpose is to determine how increasing weight impacts the friction force. To do this, we will add more weight to the iOlab gadget to prevent it from sliding about. The gadget will next be pushed against
a flat surface to test how it reacts.
We'll also consider how the forces pulling down (gravity) and up (the surface) interact with one another.
We'll use a formula to calculate the force of friction: Ff = FN. The is the coefficient of kinetic friction, which is affected by the materials in contact. We'll see if this coefficient remains constant as we increase
weight.
In brief, this lab helps us understand how weight impacts friction and allows us to calculate the friction coefficient, which remains constant regardless of how much material we add.
Method To begin the experiment, I determined the weight of the iOLab equipment. I then attached a screw to the iOlab and positioned it vertically along the y-axis. I hung the iOlab by the screw after turning on the recording, allowing it to hang for a little moment before gently returning it to its original place. I used a modified version of Newton's second law of motion to determine the iOlab's mass, employing the recorded average force and acceleration that acted on the device during this procedure.
m
=
F
a
Figure 1: The force and acceleration on the iOLab device when lifted by the y- axis.
Next I calculated the coefficient of friction as I pushed the device with the wheels facing up.
Figure 2: The acceleration on the device when pushed to the y direction.
During the experiment, I taped another object to the device's wheel side with scotch tape. I performed the mass measurement process, but this time I included the item. Then, using this new approach, I measured the acceleration of a push. Figure 3: The force and acceleration on the IOLab device with an object attached to it. This system is
lifted towards the y axis for a few seconds.
Figure 4: The acceleration of the IOLab device with an object attached to it. This system is experiencing a
push on the y direction.
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Next I repeated the previous procedure but with a second object attached to the iOLab device. Figure 5: The force and acceleration on the IOLab device with two objects attached to it. This system is
lifted towards the y axis for a few seconds.
Figure 6: The acceleration of the IOLab device with two objects attached to it. This system is
experiencing a push on the y direction.
All of the charts shown above were used to compute the normal force using gravity. I utilized all of the calculations to generate an excel graph with a linear trendline showing the force of friction vs. normal force. The average coefficient of friction for each mass was then computed. Then I computed the coefficient of friction using the slope of the force friction vs. normal force graph and compared it to the calculated value.
Result
Figure 7: This table contains all the results of the procedures done on the IOLab device with three
different mass.
Figure 8: This graph shows the force of friction vs. normal force of the IOLab device after experiencing
pushes when external mass is added. It also contains error bars vertically and horizontally.
Figure 9: This diagram shows the forces acting on the IOLab device it is pushed towards the y axis. Calculations
Mass of the iOLab device (only):
m
=
F
g
g
m
=
−
1.953
N
−
9.790
m
/
s
2
m
=
0.1995
kg
Normal force of the iOLab device (only):
F
N
=
mg
F
N
=
0.1995
kg
∗(−
9.790
m
/
s
2
)
|
F
N
|
=
1.95
N
Force of friction on the iOLab device (only) when pushed:
F
f
=
ma
F
f
=
0.1995
kg
∗(−
0.920
m
/
s
2
)
|
F
f
|
=
0.1835
N
Coefficient of friction acting on the device (only):
μ
=
F
f
F
N
μ
=
0.1835
N
1.95
N
μ
=
0.0941
Average of all coefficent of frictions:
Avg.of μ
=
μ
1
+
μ
2
+
μ
3
¿
of trials
Avg.of μ
=
0.0941
+
0.1444
+
0.1447
3
Avg.of μ
=
0.1277
Trial
Δ
mass (kg)
Δ
F_f (N)
Δ
F_g (N)
1
0.0029
0.0659
0.020
2
0.0083
0.0664 0.054 3
0.0111
0.08728
0.072
Figure 10: This table shows the error propagation of all the estimated measurements on all three trials
on this experiment including the quantities produced from those estimated measurements
Finding the error in mass: Δ m
=
m
√
❑
Δ m
=
0.1995
kg
√
❑
Δ m
=
0.0029
Finding the error in force of friction:
Δ F
f
=
F
f
√
❑
Δ F
f
=
0.1835
N
√
❑
Δ F
f
=
0.0659
N
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Discussion:
By gradually adding mass to the iOLab gadget and evaluating its behavior during both vertical lifting and horizontal pushing, the experimental approach intended to study the link between mass, friction, and the coefficient of friction. The results created a large dataset that allowed for a thorough study.
Mass Determination:
Initially, determining the mass of the iOLab gadget was critical since it served as the baseline for subsequent computations. I calculated the device's mass as 0.1995 kg using a modified version of Newton's second law.
Coefficient of Friction with a Single Object: The next step was to calculate the coefficient of friction while the iOLab gadget was pushed upward with
its wheels pointing up. This phase's data gave vital insights into the link between additional mass and friction.
Coefficient of Friction with Two objects: For further development on the experiment, we added two items to the iOLab gadget and measured them again. This allowed us to see how the coefficient of friction changed as the mass rose.
Calculating the Coefficient of Friction:
●
The computed coefficient of friction for the iOLab gadget with one item connected was 0.0941.
●
The coefficient of friction increased to 0.1444 for the first object and 0.14473 for the second object when two objects were added.
Coefficient of Friction vs. Normal Force: An Excel graph with a linear trendline was created to show and summarize the connection between the force of friction and the normal force (Figure 8). This graph demonstrated that as the normal force grew (because to the extra mass), so did the force of friction. This graph's slope allowed us to compute the coefficient of friction for each mass combination.
Average Friction Coefficient:
The average coefficient of friction was discovered to be roughly 0.1277 throughout all experiments, which included one item, two objects, and three distinct mass situations. This average was a good starting point for learning how friction behaved in different mass situations.
Error Analysis: The error analysis indicated our measurements' precision:
●
The mass error of all three systems are approximately 0.0029 kg, 0.0083 kg, 0.0111 kg respectively .
●
The force of friction error in all of the systems are about 0.0659 N, 0.0664 N, 0.08728 kg respectively .
These mistakes give important information on the dependability and quality of the experimental results.
Our measurements were consistent and dependable, based on the comparatively tiny errors.
Comparison to estimated Values: The estimated coefficients of friction using the slope of the force of friction vs. normal force graph were very similar to the experimental values, confirming the validity of our experimental technique.
Finally, the experiment indicated that the coefficient of friction between the iOLab device and the surface rose with additional mass, validating the predicted mass-friction connection. The data and computations reported in this paper provide vital insights into the physical parameters that regulate the behavior of moving objects, allowing for a better understanding of the underlying principles of friction. The slope of force of friction and the normal force represent the coefficient of friction of the average of all the systems.
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