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LAB: Newton’s Second Law
One of the most important equations in physics is ∑𝐹 = 𝑚𝑎⃑, also known as Newton’s second law of motion. It states that
an unbalanced or net force applied to a mass produces acceleration. Newton’s second law describes the behavior of
everything that changes its motion due to a net force, from the trajectory of a baseball to the motion of a planet. Because
of friction, this law seems to contradict common experience. In riding a bicycle, for example, a constant force is required
to keep the bicycle moving with a constant velocity. If the force is removed, the force of friction brings the bicycle to a
stop. In the absence of friction, however, the bicycle would continue to move with constant velocity after the force is
removed. A continued application of force would then result in acceleration. According to Newton’s second law, the net
force is only one of two factors that determine the acceleration. The other is the inertia (or mass) of the object. Newton’s
second law states that the acceleration of an object is inversely proportional to the mass and directly proportional to the
net force. Twice the mass means one-half the acceleration, if the same net force acts on the object. Twice the net force
means twice the acceleration, if the mass of the object remains constant.
The purpose of this investigation is to study the law of acceleration.
• In Part I you will measure the acceleration of an object when the net force is varied but the total mass of the
system remains constant.
• In Part II of the lab, you will determine what happens to the acceleration of the cart when the net force remains
constant and the total mass varies.
• In Part III, you will determine the frictional force acting on the cart and the coefficient of friction.
In the previous discussion of Newton’s second law it was stated that the acceleration of an object was proportional to the
net force acting on it. Often, several forces act on an object simultaneously. In such cases, it is the net force, or the vector
sum of all the forces acting, that is important. Newton’s second law states that the acceleration is proportional to the net
force acting on the object. We have previously assumed that no friction acted on the cart; however, if your track is
perfectly level and no other errors occur during the collection and analysis of data, the results probably will be lower than
the theoretical value for the acceleration. This lower acceleration is due to the force of friction, which always opposes the
motion of the cart.
During the activity you will quantify the relationships among force, mass and acceleration such that you will be able to:
• Interpret data from a graph of velocity versus time to find acceleration.
• Measure the acceleration of an object with a constant mass when the net force is changed.
• Measure the acceleration of an object when a constant net force is applied and the mass is increased.
• Calculate theoretical values for acceleration based on net force and mass and compare the theoretical values
with the measured values.
• Calculate the frictional force acting on the cart along with the coefficient of friction between the cart and the
track.
Purpose:
The purpose of this lab is to investigate the relationships between force, mass and acceleration.
Set-Up:
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Lab Pro® interface
Computer with Logger Pro® software
VERNIER Motion Encoder Cart and track
Low Friction pulley with string pulley string
Electronic balance
Slotted or hooked mass set
Procedure:
PART I: CONSTANT MASS, VARIABLE FORCE
1. Place the track so that one end is at the edge of the lab table.
2.
Make sure the track is level and stays level throughout the lab exercise. If the cart does not roll when
placed freely on the track, it can be assumed the track is level.
3.
Using a pulley clamp, secure the end of the track to the table and place a pulley into the clamp. The
pulley should be adjusted so that the string remains level as the cart moves along the track.
4.
Attach a string to the cart and pass the string over the pulley at the edge of the table. The string should
be just long enough so that when the cart reaches the end of the track, the mass hanger just reaches the
floor. Tie a loop in the string if using hooked masses, or tie the hanger to the string if using slotted
masses.
5.
The motion encoder system must be configured manually. This ensures that a proper data collection is
performed on the cart as it moves along the track. Listen to your instructor’s comments on whether or
not this process needs to be completed.
6.
Using Logger Pro on the computer empty graphs of position vs. time and velocity vs. time should
appear on the computer screen. Press Collect on the toolbar. Test roll the cart down the track to make
sure the encoder system is correctly configured to locate the cart. Stop the cart before it hits the pulley
and click Stop. Always catch the cart before it hits the pulley or you could damage the pulley.
7.
Mass the cart and string. Also mass the mass hanger if you are using one. Record these masses in Data
Table 1 on your student answer page.
8.
Obtain three equal masses. These three masses will remain in the cart/string system throughout all three
runs so that the total mass of the system remains constant.
9.
Move the cart to the end of the track and place it in front of the encoder interface.
10. One lab partner should use their finger to hold the cart on the track until it is time to release. For Run #1
the other lab partner should position two masses on the cart and one mass on the string. Be sure the
string is still before continuing.
11. Press Collect on the Logger Pro toolbar. Quickly remove your finger from the cart and allow it to move
down the track. Be sure to stop the cart before it hits the pulley. Press Stop on the Logger Pro toolbar
once you have stopped the cart.
12. Note the shape of the position time graph. What does the shape indicate? What about the velocity vs.
time graph? What does its shape indicate?
13. Using the mouse, click and drag a box over the portion of the velocity vs. time graph where the cart was
being accelerated by the hanging weight. Click on the R= analysis tool to find the linear regression line
that best fits your data. Record the slope of the velocity vs. time graph in Data Table 1 along with the
mass and force data for each run.
14. For the second and third runs, transfer one mass from the tray of the cart to the mass hanger on the
string. Run #2 should have 1 mass on the cart and 2 on the hanger. Run #3 should have no masses on
the cart and all three on the hanger.
PART II: CONSTANT FORCE, VARIABLE MASS
1.
Using the same equipment set up in Part I, re-verify that the track is still level. Remember to catch the
cart before it hits the pulley or you could damage the pulley.
2.
Add a 20-g mass to the mass hanger and weigh the hanger plus the mass. Record the mass in Data Table
2.
3.
Mass the cart and record its value in Data Table 2.
4.
You will take three runs of data. For Run #1, use one 20-g mass on the mass hanger.
5.
Click Collect and release the cart. Stop the cart before it hits the pulley and click Stop.
6.
Analyze the data using the procedure described in Part I. Click the Auto scale button if needed
Using the mouse, click and drag a box over the portion of the velocity vs. time graph where the cart was
being accelerated by the hanging weight. Click on the R= analysis tool to find the linear regression line
that best fits your data. Record the slope of the velocity vs. time graph in Data Table 2 along with the
mass and force data for each run.
7.
For Run #2, add a 500-gram rectangular cart-mass to the cart. The total mass of the system is increased,
but the net force from the string is the same. Record the new total mass of the cart. Analyze and record
your data as you did in Run #1.
8.
For Run #3, add a second 500-g mass to the cart. Record the new total mass of the cart. Analyze and
record your data.
PART III: FRICTION
1. Using your experimental data, calculate and examine the effects of friction by completing the Analysis
questions in Part III of your handout.
Data:
Analysis:
PART I: CONSTANT MASS, VARIABLE FORCE
1.
Draw two separate free body diagrams for the cart and for the hanging mass.
2.
Beginning with Newton’s 2nd Law, develop an equation for the acceleration of the cart-hanging mass system.
Show all of your steps and express your answer in terms of g (acceleration due to gravity, m c (mass of cart and
what rests on it) and mh (mass of hanging object).
3.
Using your answer to question 2, Calculate the theoretical acceleration when mass is constant and net force is
changed. The theoretical acceleration is the ratio of the net force divided by the total mass. For Part I the total
mass of the system (mass of cart plus mass of hanger) is constant and the net force increases. Assuming no
friction, the net force is the weight of the hanger (mass × 9.81). Record your values in Table 3.
4.
The percent difference is the absolute value of the difference between the theoretical acceleration and the
experimental acceleration divided by the theoretical acceleration. Use your experimental acceleration from the
slope of the v vs. t graph from table 1 above. Record your values in Table 3.
PART II : CONSTANT FORCE, VARIABLE MASS
1.
Using your answer to question 2 in the previous analysis section, calculate the theoretical acceleration when net
force is constant and mass is changed. Record your values in Table 4.
2.
The percent difference is the absolute value of the difference between the theoretical acceleration and the
experimental acceleration divided by the theoretical acceleration. Use your experimental acceleration from the
slope of the v vs. t graph from table 2 above. Record your values in Table 4.
PART III: FRICTION
1. Find the force of friction in each of your runs for Part I of the lab and record the value in Table 5. Do this by
subtracting the actual acceleration from your theoretical acceleration value for each run. If we assume the
difference in acceleration is due to friction, then the value for the frictional force should be:
𝐹𝑓 = 𝑚𝑐𝑎𝑟𝑡 ∙ ∆𝑎
2.
The coefficient of friction is the ratio of the force of friction to the normal force acting on the system. Calculate
the coefficient of friction for each of the runs in Part I. Record your values in Table 5. We may assume that the
normal force 𝐹𝑁 is the weight of the cart. For our purposes, we will still assume that the pulley is frictionless and
that all the friction is due to the cart.
𝜇=
𝐹𝑓
𝐹𝑁
3.
Using the three runs from Part I of the lab, find the average value for the coefficient of friction for the system
used in this lab.
Questions:
1.
What evidence allows you to know if the acceleration was proportional to the force? Explain your answer by
referring to specific results from your experiment.
2.
What evidence allows you to know if the acceleration was inversely proportional to the mass? Explain your
answer by referring to specific results from your experiment.
3.
Would the presence of an additional mass in the cart during all the runs increase, decrease, or not affect the
slope of the velocity time graph? How could you use this experimental set-up to find the value of the
additional mass that was in the cart?
4.
Suppose the string breaks as the cart accelerates one-third of the way across the track. What is the
acceleration of the cart for the remaining length of track? Explain.
5.
Theorize what would happen to your results if the ramp was raised at a slight incline. Would the
acceleration change and if so how would it change?
Conclusion:
In your own words (not your lab partner’s words), explain what you did in this lab, how you did it, why and results. Use
appropriate vocabulary. Remember this is a summative lab, so this section is very important. You may want to break the
conclusion into 3 parts, one for each part of the lab.