Download Newton`s Second Law with Constant Mass

EXPERIMENT 5
NEWTON’S SECOND LAW WITH A CONSTANT MASS
Objectives
1. To find the acceleration of a cart using the graph of its velocity versus time
2. To establish a mathematical relation between the acceleration of an object and the applied force when the
mass of the object is held constant
3. To calculate the acceleration of an object given the net force and mass, and then compare it to the
experimental value, and
4. To verify the relation between the acceleration, mass and net force on an object subjected to linear motion.
Theory
An important equation in physics is the mathematical form of Newton’s second law,
F = ma
Where F is the net external applied force on an object of mass m and a is the resulting acceleration. Note that F
and a are vectors. This law establishes the fact that only an external unbalanced force will cause an object to move
and accelerate. The purpose of this experiment is to find out what happens to the acceleration of an object of mass
m if an external force is applied. We will use a motion sensor to study the object motion while an external force is
acting it upon. We will determine what happens to the acceleration of the object when the net force is changed
while keeping the mass of the object constant. We shall keep in mind that the acceleration of the object is defined
as the change of velocity with time i. e. it is the derivative of its velocity with respect to time.
a = lim
t →0
Δv
Δt
=
dv
dt
What happens to an object when a net external force is applied? How does the motion of an object change when
the magnitude of this force is changed? Newton’s first law states that if the net force on an object is zero, then the
object is at rest or moves with a constant speed with no change in its direction. The second law states that when a
net force is not zero then the object will accelerate. If the external force is increased the acceleration will increase
(assuming constant mass). If the net force is doubled, the acceleration is doubled i. e. the net force is directly
proportional to the acceleration.
F∝a
Oftentimes, several forces act on an object simultaneously. In such cases, the vectorial sum of all the forces is
the relevant force. Also, Newton’s second law states that the acceleration is inversely proportional to the mass.
a ∝ 1/m
Equipment
Motion sensor
Pasco 750 Interface
Set of masses
Track
1
1
1
1
Balance
Pulley with string
Cart track
Juan A. González and Claudio Guerra‐Vela. Department of Physics and Electronics. University of Puerto Rico at Humacao. Sponsored by the National Science Foundation (NSF) © All rights reserved 2006 1
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Procedure
Figure 5-1. Leveled cart track. The cart must remain at rest at any point on the track
1.
2.
3.
4.
5.
Level the cart track on a horizontal table by adjusting the levelling screws. Make sure the cart is stationary at
any position on the track. See Figure 5-1
Note that the track is designed to accomodate the motion sensor at either end. Install a motion sensor at one
end
Install the pulley at the other end and use a piece of wood to prevent the cart from hitting the pulley
Tie a string (about 1.2 m in length) to the cart and pass it over the pulley. See Figure 5-2
Measure the mass of the mass holder
Experiment 1:
1. Place a 20 g mass on the mass holder. Write the total mass attached to the mass holder, in Table 1 of your lab
report
2. Measure the mass of the cart
3. Place two masses of 20 g each on the cart
4. In your lab report, write the mass of the cart plus 40 g of the additional masses
5. Check that the setup of your experiment looks as that shown in the Figure 5-2 below
Figure 5-2. Complete experimental setup for Newton’s Second Law
6.
7.
8.
9.
Adjust the pulley so that the string is parallel to the track
Keep the cart a distance of at least 15 cm from the front of the sensor before releasing it
You will do three experiments using the above mentioned setup:
i.
In the first experiment you have 20 g on the mass holder and 40 g on the cart,
In the second experiment, transfer 20 g from the cart on to the mass holder. The total mass of the
ii.
system is constant but the net force increases,
iii.
In the third experiment, transfer the other 20 g from the cart on to the mass holder. Once again the
total mass of the system is constant but the net force increases
Note: Remember to catch the cart before it hits the pulley or you may damage the cart and pulley
Press the “Start” button. Release the cart. Stop the cart before it hits the pulley and press the “Stop” button
to stop the program. In the analysis section you will learn how to analyze the data
Experiment 2.
10. For the second graph, remove 20 g from the cart and place it on to the mass holder. Write the total hanging
mass in table 1 of your lab report
Experiment 3.
11. For the third graph, remove the 20 g from the cart and place it on the mass holder. Write the total hanging
mass in your lab report
Juan A. González and Claudio Guerra‐Vela. Department of Physics and Electronics. University of Puerto Rico at Humacao. Sponsored by the National Science Foundation (NSF) © All rights reserved 2006 2
Analysis
Graphical analysis
1.
2.
3.
4.
5.
Press “Adjust Scale” to make the graph appear more accurate if necessary. Use the cursor to select the
linear portion of the curve
Select “fit” from the menu and select the “linear fit” option. The slope “m” of the selected linear portion of
the graph is the acceleration
After calculating the slope of the graph in Figure 3 use the data menu to select the other graphs. The
example in the plot below shows the linear fit and the fitting parameters
Make a note of the slope which is the acceleration for all the graphs
Follow the same procedure to calculate the acceleration for all of the graphs
Figure 5-3 The slope of this line is the acceleration of the cart
Juan A. González and Claudio Guerra‐Vela. Department of Physics and Electronics. University of Puerto Rico at Humacao. Sponsored by the National Science Foundation (NSF) © All rights reserved 2006 3
Laboratory Report Of Experiment 5
Newton’s Second Law with a constant mass
Section _________ Bench________
Students
1. _________________________________________________________________________
2. _________________________________________________________________________
3. _________________________________________________________________________
4. _________________________________________________________________________
1.
Write the mass of the mass holder mh = _____________kg
2.
Add 20 g to the mass holder and write the total hanging mass and net external force in Table 1 for the three
experiments. Also add 40 g to the cart
3.
Fill out the remaining blanks in Table 1 with the data for experiments 2 and 3. Remember that you will
transfer 20 g of mass from the cart to the mass holder each time
Experiment
Mass of mass holder + added
mass (kg)
Table 1
Calculated net external
force
F = ma (N)
Total mass in cart = mass
of cart + added mass (kg)
1
2
3
4.
Follow the procedure to graph the velocity of the cart versus time. Find the acceleration from the graph and
enter its value in Table 2 below. Repeat the procedure for the other two experiments
Juan A. González and Claudio Guerra‐Vela. Department of Physics and Electronics. University of Puerto Rico at Humacao. Sponsored by the National Science Foundation (NSF) © All rights reserved 2006 4
Table 2
Graph
Slope = Acceleration (m/s2)
1
2
3
Data Analysis
1.
What do you conclude from the slopes of the graphs when the net force on the cart increased but the total
mass of the system remained constant?
2.
Calculate the acceleration of the cart when the total mass of the system is held constant but the force changes.
Use the equation below. The acceleration is the net force divided by the total mass
acalculated =
Acceleration
(Calculated)
(m/s2)
3.
(mhanger + madded ) g
mtotal mass in cart + (mhanger + madded )
Table 3
Acceleration
(Experimental)
(m/s2)
% Error
Draw a new graph of the net force (N) versus the acceleration (m/s2) of the cart and calculate the % error of
the total mass used (measured using a balance) and the total mass obtained from the slope of this graph.
m=
ΔF
Δa
Juan A. González and Claudio Guerra‐Vela. Department of Physics and Electronics. University of Puerto Rico at Humacao. Sponsored by the National Science Foundation (NSF) © All rights reserved 2006 5
Total mass obtained
using a balance (kg)
4.
Table 4
Mass obtained from the
slope of the graph (kg)
% Error
What are your conclusions when the data are compared?
Discussion
1.
What variable (mass or force) did you keep constant during the experiment, and what variable did you
change? Explain your answer
2.
What variable changed as a result of keeping one constant?
Juan A. González and Claudio Guerra‐Vela. Department of Physics and Electronics. University of Puerto Rico at Humacao. Sponsored by the National Science Foundation (NSF) © All rights reserved 2006 6
Error analysis
What are the sources of error in the experiment?
Conclusions
1.
What happens to the acceleration of the object (mass constant) if the net force is increased?
2.
Does your experiment support this claim?
Supplemental Problem
A bicyclist has a mass of 87.1 kg, and his cycle has a mass of 13.1 kg. The bicyclist pedals his bicycle with a net
horizontal force of 9.78 N. What is his acceleration?
Juan A. González and Claudio Guerra‐Vela. Department of Physics and Electronics. University of Puerto Rico at Humacao. Sponsored by the National Science Foundation (NSF) © All rights reserved 2006 7
Questions on Experiment 5
Newton’s Second Law with a constant mass
This questionnaire has some typical questions on experiment 5. All students who are taking the laboratory
course of University Physics I must be able to correctly answer it before trying to make the experiment.
1.
In a graph of velocity versus time, the slope gives:
a. Instantaneous velocity
b. Instantaneous acceleration
c. Instantaneous position
d. No known quantity
e. Force
2.
The velocity of an object is given by the following function v(t) = t2 + 3t - 9 where t is the time in seconds.
The acceleration of the object after 4 s is:
a. 11 m/s2
b. 19 m/s2
c. Zero
d. Cannot calculate, insufficient information
e. 4.75 m/s2
3.
A larger acceleration requires:
a. Larger mass
b. Larger force
c. Smaller mass
d. Smaller force
e. Not possible to tell
4.
A 20 kg object accelerates at 5 m/s2. The force required to maintain the acceleration constant is:
a. 50 N
b. 4 N
c. 100 N
d. There is no force
e. 35 N
5.
A net force of 2800 N is applied to a 1400 kg automobile at rest. The speed of the automobile after 10 s will
be:
a. 2 m/s
b. 5 m/s
c. 10 m/s
d. 20 m/s
e. 3 m/s
6.
The following graph of velocity versus time represents that of an automobile that travels in a straight line.
The distance traveled in the time interval between 2 s and 5 s is:
Figure 4 A graph of velocity vs. time
Juan A. González and Claudio Guerra‐Vela. Department of Physics and Electronics. University of Puerto Rico at Humacao. Sponsored by the National Science Foundation (NSF) © All rights reserved 2006 8
a.
b.
c.
d.
e.
7.
4m
12 m
24 m
36 m
60 m
The following graph of velocity versus time represents that of an automobile that travels in a straight line.
From this graph one can conclude that:
Figure 5 A graph of velocity vs. time
a.
b.
c.
d.
e.
The automobile accelerates, then stops and then reverses direction
The automobile accelerates at 6 m/s2 during the first 2 s
The automobile moves for a total of 12 s
The automobile decelerates at 12 m/s2 during the last 4 s
The automobile returns to the starting point after 9 s
8.
The mass of a salami of 3 lb is:
a. 0.31 kg
b. 1.36 kg
c. 6.6 kg
d. 29.4 kg
e. 19.2 kg
9.
One (1 kg)(1 m/1 s2) is equivalent to:
a. 1 m/s
b. 1 Newton
c. 1 Joule
d. 1 vector
e. 1 volt
10. The weight of an object is:
a. The amount of mass that it contains
b. The force with which it is attracted to the earth
c. Basically the same as the mass but acts in the opposite direction
d. A measure of its inertia
e. Something that has the same value on any other planet
Juan A. González and Claudio Guerra‐Vela. Department of Physics and Electronics. University of Puerto Rico at Humacao. Sponsored by the National Science Foundation (NSF) © All rights reserved 2006 9