Download Newton`s Second Law of Motion

普通物理實驗講義
Newton’s Second Law of Motion
Objective
1.
2.
To prove Newton’s second law of motion by observing the force-driven
movement of a glider.
To understand the linear regression data processing method and learn the
adjustment methods for horizontally leveling air tracks.
Principles
A. Adjustments for horizontal leveling
When an air track is not level and pressure is not exerted on the glider, external
forces (such as the field of gravity) have already acted on the glider. Therefore, to
reduce experiment complications, the horizontal level of the air track should be
adjusted before the experiment. Additionally, based on the uniform accelerated motion
of kinematics, we know that:
v 2 = v0 2 + 2 aS
(1)
When a constant force acts on an object, the object generates equal constant
acceleration, which varies at different locations. Therefore, by adjusting the air track to
be horizontally level, acceleration at various locations on the air track will be uniform.
B. Newton’s second law of motion
When force from a weight is exerted on a glider on an air track (Fig. 1), the
equation of motion is:
r
r
r
F = mg = ( m + M ) a
(2)
v
where m g is the external force acting on the system, (m+M) is the mass of the
v
system, and a is the acceleration of the system generated from the external force.
Therefore, we formulated the following assumptions based on Newton’s second law of
motion:
1. When the mass of a system is fixed, the external force is proportional to the degree
of acceleration.
2. When an external force is fixed, the mass of a system is inversely proportional to
the degree of acceleration.
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Figure 1
Apparatus
1.
2.
3.
4.
5.
6.
One air track
One air pump
One glider
One component box (including rubber bands, cotton string, and weights)
One optical timer
Two photothyristors
Precautions
The air track used for this experiment was a hollow, triangular track with fine holes
evenly distributed across the surface. An air pump was used to pump air through these
fine holes, as shown in Fig. 2. The surface of the air track must remain smooth to
reduce friction against the glider.
To prevent damage to the air track, students should abide by the following rules:
※ Before placing the glider on the track, ensure that the air pump is activated and air
is being pumped through the fine holes of the track surface.
※ Do not overload the glider on the air track.
※ Remove the glider from the air track before deactivating the air pump.
Figure 2
Procedures
A. Understanding the operation methods of the optical timer and photothyristors.
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Figure 3
B. Adjusting the horizontal level of the air track
1.
2.
3.
4.
Select two locations on the air track (locations A and B) and place an optical
gate at each of these locations.
Tie rubber bands at fixed locations to provide fixed elastic force, as shown in
Fig. 3. When the hand holding the glider secure is lifted, the glider should
glide forward, sequentially passing through the photothyristors at locations A
and B. Calculate the velocity v = ∆ x / ∆ t of the glider between locations A
and B, where x is the width of the deflector on the glider used to deflect the
photothyristors (if no deflector is available, the body of the glider can be used
to deflect the optical gate; in this case, x is the length of the glider), and t is the
time of deflection.
Repeat procedure 2 three times to obtain the average velocity v between
locations A and B.
Compare the difference in v value between locations A and B, and determine
the horizontal level of the track. (If the track is not horizontally level, adjust
the front or back end of the air track and repeat procedures 2 to 4 until
horizontal leveling is achieved.)
C. Proving Newton’s second law of motion
C-1. The association between glider mass M and acceleration a
1. Tie one end of a string to one side of the glider and the other end to a
hooked weight (Fig. 4).
2. Another cotton string can be tied to the other side of the glider to facilitate
the release of the stationary glider.
3. Arrange the two photothyristors in an appropriate distance from each other
to ensure that the glider can pass through both gates when the weight is
dropped.
4. Record the relative position between the two photothyristors from the
starting point of the glider.
5. Determine the glider mass M and weight mass m, and measure the glider
acceleration a. Numerous iterations of these measurements should be
performed to obtain more objective results.
6. Change the glider mass M five times, and repeat procedure 5.
7. Plot a graph by applying 1/(M+m) as the horizontal axis and a as the
vertical axis.
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8. Apply the least squares method to determine the linear regression equation;
subsequently, compare the theoretical values to the intercept and slope of
the resulting regression line.
C-2. Weight mass m and glider acceleration a
1. Under a weighed force of a certain mass m exerted on the glider, measure
the glider acceleration a. These measurements should be performed
numerous times to obtain more objective results.
2. Change the weight mass m at least five times.
3. To achieve a linear association in the final data, a fixed value for the sum
of M+m is suggested.
4. With m as the horizontal axis and a as the vertical axis, determine the
linear regression equation using computer graphics software. Then,
compare the theoretical values to the intercept and slope of the resulting
regression line.
Reflection of the Problems
1.
During the experiment, adjusting the horizontal level of the air track is extremely
important. Please record your experiences and comments on how to quickly and
efficiently adjust the air track.
2.
Based on the regression lines obtained in experiments C-1 and C-2, explain the
physical significance of the intercepts and slopes.
3.
Suppose that the air track is tilted at angle; consequently, friction is also present in
the system. How can Eq. (2) be amended? Additionally, how would the plotting of
graph 1/(M+m) and a reflect this error?
4.
Besides a tilted air track and friction, list other factors that may cause
experimental errors.
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