INQUIRY PHYSICS
inquiryphysics.org
A Modified Learning Cycle Curriculum
by Granger Meador, ©2010
Unit 5:
Force and Acceleration
Teacher’s Guide
Student Papers
Sample Notes
5 Force and Acceleration
Teacher's Guide
Inquiry Physics
Key Concepts
An object subjected to a constant force (over any distance) will experience a constant acceleration which
is directly proportional to the size of the unbalanced force.
Student Papers
Lab A: Acceleration Due to a Constant Unbalanced Force:
Air track version
Dynamics cart on floor version
Dynamics cart with table pulley version
W orksheet: Concepts & Calculations
Lab B: Varying Forces and Acceleration:
Air track version
Dynamics cart on floor version
Dynamics cart with table pulley version
Introduction
Four labs, two in this unit and two in the next, culm inate in the students deriving the Newton's Second Law
of Motion (Law of Acceleration; F=m a). You will want to keep rem inding the students of previous results
as you build toward that goal.
Throughout the labs in this unit, the m ass concept is to be scrupulously avoided, so as not to short-circuit
concept developm ent in the following unit. If a student m entions m ass, do not go into that topic, and don't
be afraid to act as though kilogram s is a unit of weight for now. In the next unit, the students will
conceptualize m ass and the distinction between kilogram s and newtons will be m ade. Also, m any
students are not form al-operational and cannot accept that balances can m easure m ass even though they
are really m easuring weight (because m g for one side equals m g for the other and the g will cancel out).
LAB A: Acceleration Due to a Constant Unbalanced Force
Exploration
Equipm ent for each group (of 3 to 4 students):
Air track version:
1.5 m or longer air track with end pulley
1 red 300 g glider
stopwatch
string/fishing line
hanging weight holder
Dynam ics cart on floor version:
dynam ics cart (taping weights onto each cart beforehand
to m ake it a convenient weight can save lab tim e)
5 N and/or 20 N spring scale
m eterstick
long spring (perhaps cut a worn-out wave dem onstrator
spring like the one at the far right to 50 cm ;
avoid Slinkies, which are too large, and
rubber bands, which don't have a constant
force/stretch ratio)
tape (or thum btack or sm all nail) to secure spring to m eterstick
enough weights to bring loaded cart up to 6 kg
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Dynam ics cart and table pulley version:
dynam ics cart (taping weights onto each cart beforehand to m ake it a
convenient weight can save lab tim e)
table pulley
string/fishing line
hanging weight holder
m eterstick
enough weights to bring loaded cart up to 6 kg
If using air tracks, use a sm all hanging weight or the runs will be too fast for the stopwatches. You m ay
wish to use fancy tim ing equipm ent, but be careful not to allow fancy equipm ent to do the thinking for the
students; calculating accelerations from stopwatch readings is a useful approach since it is easily
generalized by students to all m otions and reinforces the use of a = 2d/t2 when v i=0. Leveling the track is
crucial, as is not allowing the hanging weight to swing as it falls nor letting it reach the floor.
If using the dynam ics carts on the floor, students m ay need help keeping the force constant as they
accelerate the cart. Observe them to ensure that they are keeping the spring stretched the sam e length
along the m eterstick throughout the entire trip; they will have a tendency to slack off as the speed builds
and this can lead to large experim ental error. Encourage students to check each other as the lab
progresses. Feel free to adjust the cart weight and spring forces as necessary for your equipm ent and to
m inim ize error.
If using the dynam ics carts with a table pulley, m ake sure your runs are long enough so that tim ing errors
are not too great, and be sure to run a trial lab yourself beforehand to ascertain which distances the class
should use. Feel free to adjust the cart weight and hanging weight as needed to get decent results.
The purposes in changing the distance and not the force are: 1) to let students see that distance is
independent of acceleration, so d can be changed without affecting a m easurem ents; 2) to let students
see what a "null result" looks like (they will usually struggle to interpret experim ental error in this lab as
evidence of som e relationship between d and a); and 3) for the dynam ics cart version of the lab, this lab
provides experience in keeping the force constant through varied distances to im prove their work in Lab B.
Supervise the com pletion of the tables in each group. Be sure they calculate the average accelerations
correctly, for this is the data you will use to invent the concept that a constant force produces a constant
acceleration, so be m eticulous about how the table is com pleted.
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The Idea
The analysis is m ore detailed in the air track version, as it provides m ore data points of greater accuracy
and precision than the other versions.
Lab A Sample Answ ers for AIR TRACK version
a = 2d / t2
1.
Show the motion equation you used to calculate acceleration: ?
2.
Plot the data points for your group’s data to help you see the relationship, if any, between the changing
distance and the calculated acceleration. Plot the independent variable on the x-axis and the dependent
variable on the y-axis. Force each axis to begin at zero.
Notice the difference between this graph and the two graphs you generated from the data in lab 1 (the ball
rolling down the ramp). Save your graph and show it to your teacher, but do not print it out unless directed
to do so.
3.
One way to quantify how much change there is in a variable is to calculate the percentage difference. The
formula is shown below. W hat is the percentage difference if some arbitrary independent variable doubles?
(Make up some numbers and plug them into the formula; you need not use lab data here.)
varies
4.
Consider a hypothetical linear graph, or directly proportional relationship. If you doubled
the independent variable, the dependent variable should also double. So if you had a
directly proportional relationship and the independent variable doubled, what percentage
difference would you expect to see for the dependent variable?
5.
For directly proportional relationships, tripling the independent variable triples the dependent, and so forth.
Thus we can generalize the concept from questions 3 and 4. W hen there is a directly proportional
relationship, what should one expect when comparing the percentage difference of the independent variable
to that of the dependent variable?
varies
The percentage differences for each variable should be similar.
6.
You will need the class average accelerations to answer questions 6-9. Quantify how much change there
was in the class average accelerations by calculating the percentage difference between the highest and
lowest class average values. (W e cannot calculate percentage error in this situation, as we do not know the
theoretical values.) Show your work:
Results will vary, but should not be nearly as large as 40%. (Because there
is no relationship between distance and accel. when force is constant.)
7.
To help you put this in perspective, calculate the percentage difference between the highest and lowest
distances. Show your work:
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8.
Bear in mind your answer to question 5. Does the class data indicate a directly proportional relationship
between acceleration and distance? Explain why or why not.
No, because their percentage differences are not similar.
9.
After considering a graph of the class data and the answers to questions 6-8, precisely describe what an
object does when a constant, unbalanced force is applied to it.
An object accelerates at a constant rate, regardless of distance, when a
constant, unbalanced force is applied.
10.
W hat are the significant sources of systematic error in this experiment?
Timing and friction are the major systematic errors.
Lab A Sample Answ ers for DYNAM ICS CART versions (either on floor or w ith a table pulley)
1.
W hich equation did you use to calculate acceleration?
2.
How do the average accelerations com pare?
a = 2d / t2
They are similar.
(Using class averages is helpful here, since experimental error in a particular group can
easily disguise that the acceleration is essentially constant. You can have students put
their data on the board, possibly throw out the high's and low's or other out-of-kilter data
points before calculating averages. Students may have to be show n a rough plot of d vs. a
to see that it is forming a fairly striaght line for the class as a w hole; questions 3 and 4 w ill
hopefully make this point as well. If the data isn't good enough, discuss experimental
error sources and how to minimize them, and have the students re-do the lab! Don't
expect perfection, but don't undermine your credibility by using lousy data to invent a
concept.)
3.
W e can quantify your answer by calculating the percentage difference between the highest and
lowest values for the class' average accelerations. (W e cannot calculate percentage error in this
situation, as we do not know the theoretical values.) Show your work:
answers will vary
4.
To help you put this into perspective, calculate the percentage difference between the highest and
lowest distances. Show your work:
Dynamics cart on floor: ((1.5 m - 0.5 m)/((1.5 m + 0.5 m)/2))*100 = 100%
Dynamics cart with table pulley: answers will vary
5.
Obviously, we changed the distance quite a bit to see what effect, if any, it would have on the
acceleration of a body which is being acted upon by a constant, unbalanced force. How m uch or
what kind of effect did it have?
Changing the distance did not affect the acceleration beyond a level
explainable by experimental error.
(This is because the time w as making a corresponding change.)
6.
Precisely describe what an object does when a constant, unbalanced force is applied to it.
A constant, unbalanced force will cause a constant acceleration.
(The idea of constant accel. is vital; they already should know forces cause acceleration.)
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Expansion of the Idea - W ORKSHEET
The worksheet is a quick way to reinforce the concepts invented in Lab A and have students expand them
into other situations.
1.
How can you determ ine by watching a body whether or not an unbalanced force is acting on it?
It will accelerate.
2.
Joe m ade a toy rocket-powered car. He wanted to m easure the average acceleration of the car.
To do that, he tim ed the car over a distance of 0.500 m . He found that the car, starting from rest,
passed the 0.500 m m ark so rapidly that he could not accurately m easure the tim e. Joe's friend
Jack suggested that he increase the distance until the tim e becam e m easurable. Joe said that
changing the distance would change the m easurem ent of the acceleration, even though the car
was still m oving under full power. If you were there, how would you respond to the argum ent?
Joe is wrong; changing distance will not affect acceleration when force is
constant.
3.
Joe found that his car traveled 2.00 m eters in 0.900 seconds. W hat was the car's acceleration?
4.
Assum ing the acceleration of the car does not change, find the tim e required for the car to to 4.00
m eters starting from rest.
5.
Assum ing the acceleration and weight of the car do not change, how does the force acting on the
car change as tim e and distance increase?
It does not change.
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Expansion of the Idea - LAB B: VARYING FORCES AND ACCELERATION
Equipm ent for each group (of 3 to 4 students):
Air track version:
1.5 m or longer air track with end pulley
2 red 300 g gliders with velcro on their bum pers (or carefully brought together on an active air
track and secured with a paperclip)
stopwatch
string/fishing line
hanging weight holder
5 washers (or other sm all identically-sized weights)
Dynam ics cart on floor version:
dynam ics cart (taping weights onto each cart beforehand to m ake it a convenient weight can save
lab tim e)
5 N and/or 20 N spring scale
m eterstick
long spring (perhaps cut a worn-out wave dem onstrator spring to 50 cm ; avoid Slinkies, which are
too large, and rubber bands, which don't have a constant force/stretch ratio)
tape (or thum btack or sm all nail) to secure spring to m eterstick
enough weights to bring loaded cart up to 6 kg
Dynam ics cart and table pulley version:
dynam ics cart (taping weights onto each cart beforehand to m ake it a convenient weight can save
lab tim e)
table pulley
string/fishing line
hanging weight holder
m eterstick
enough weights to bring loaded cart up to 6 kg
slotted weights
This lab is designed to lead students to the idea that when the weight of the cart is held constant, and the
force is changed, the acceleration of the cart is directly proportional to the force acting on it. You can
either have each group analyze its own data or have them analyze a class average, or both.
If using air tracks, be careful not to use too large of a hanging weight, especially on the heaviest runs, or
tim ing errors will becom e too large. Also watch out for air tracks that start shifting off the table or
countertop as the hanging weights increase. If you really want to use fancy tim ing equipm ent, this lab is
better for that than Lab A.
If using dynam ics carts on the floor, feel free to adjust the m ass of the cart or the spring forces to suit your
equipm ent and reduce error. Em phasize the im portance of keeping the force constant throughout the
entire run, especially on the runs with larger forces. Slacking off will create unacceptable experim ental
error.
If using dynam ics carts and table pulleys, feel free to adjust the m ass of the cart and the am ount of
hanging weight to m atch your equipm ent and reduce error.
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Lab B Sample Answ ers for AIR TRACK version
1.
Does every group have to use the sam e distance to com pare their results? Explain why or why
not.
No, distance does not affect acceleration when force is constant.
(However, to maintain consistent systematic timing and friction errors, it
would be helpful to use the same distances.)
2.
Measure your hanging weight holder on the precision balance. Record the reading below:
W eight holder is
3.
varies
W e need to convert the reading into the m etric unit of weight, newtons. (The abbreviation for
newtons is "N".) Multiply the reading by 0.0098 to convert gram s to newtons. Show the new value
in the space below:
W eight holder weighs
4.
gram s.
varies
N.
Calculate the average tim e and acceleration of the glider for each run. How did increasing the
force affect acceleration?
Increasing the force made the acceleration increase.
5.
W hy is (0,0) a valid data point on your graph? (No, it is NOT because the objects started from
rest.)
When no force is applied, the object does not move (nor accelerate).
6.
The shape of your graph indicates a specific m athem atical relationship between force and
acceleration. Describe that relationship using the term inology you learned in earlier labs.
They are directly proportional. (Do not accept “directly related”.)
7.
The m athem atical relationship you have described should allow you to predict how acceleration
will change when force changes. For exam ple, if the force acting on an object doubles, what does
your graph predict will happen to the acceleration of the object?
The acceleration will also double.
8.
You should recall that the equation of a line is y=m x+b where m is the slope and b is the
y-intercept. Your graph shows the m athem atical relationship between force and acceleration.
W rite the com plete equation for your graph, using F as the sym bol for force and a for acceleration
and your graph's slope and y-intercept (properly rounded).
a = mF+b (m
w ill be their graph's slope and b should be close to zero)
9.
Let's test your answer to question 3 by checking the acceleration when the force doubles. Use
your graph's equation to find the theoretical acceleration at 0.200 N and 0.400 N of force. W rite
down those values and then com pare them m athem atically in a ratio. (Divide the larger
acceleration value by the sm aller one.) W rite your ratio down too, with 3 significant figures.
Accel. at 0.200 N =
m /s2
Accel. at 0.400 N =
m /s 2
Ratio =
to 1
(answ ers w ill vary, but their ratio should come out close to 2 to 1)
10.
Theoretically, what should the ratio be between the two accelerations? (Use your answer to
question 3 to help you answer this question. Notice the ratio of the forces we arbitrarily used in
question 9.)
It should be 2 to 1. (Sometimes they think this will be the slope of the
graph, but it is NOT that, but instead the ratio between two accelerations.)
11.
W rite a brief conclusion stating what general principle or concept this lab has illustrated.
Force and acceleration are directly proportional.
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Lab B Sample Answ ers for DYNAM ICS CART versions (either on floor or w ith a table pulley)
1.
W hy is (0,0) a valid data point on your graph?
There is no acceleration when no force is acting.
2.
The shape of your graph indicates a specific m athem atical relationship between force and
acceleration. Describe that relationship using the term inology you learned in earlier labs.
It is a linear/directly proportional relationship.
3.
The m athem atical relationship you have described should allow you to predict how acceleration
will change when force changes. For exam ple, if the force acting on an object doubles, what does
your graph predict will happen to the acceleration of the object?
The acceleration will double.
4.
You should recall that the equation of a line is y = m x+b, where m is the slope and b is the yintercept. Your graph shows the m athem atical relationship between force and acceleration. W rite
the com plete equation for your graph, using F as the sym bol for force and a for acceleration and
your graph's slope and y-intercept (properly rounded).
a = mF+b (m
5.
w ill be their graph's slope and b should be close to zero)
Let's test your answer to question 3. Use your graph's equation to find the theoretical acceleration
at one level of force and then at another level of force that is twice as large. W rite down those
values and then com pare them m athem atically in a ratio. (Divide the larger acceleration value by
the sm aller one.) W rite your ratio down too, with 3 significant figures.
Accel. at
N=
m /s2
Accel. at
N=
m /s 2
(answ ers w ill vary, but their ratio should come out close to 2 to 1)
6.
Ratio =
to 1
Theoretically, what should the ratio be between the two accelerations? (Use your answer to
question 3 to help you answer this question. Notice how you changed the force.)
The ratio should be two to one.
(If they think it is 1 to1, they are likely misinterpreting the question and/or the meaning of a
directly proportional relationship.)
7.
W rite a brief conclusion stating what general principle or concept this lab has illustrated.
(Unbalanced) force and acceleration are directly proportional.
After we discuss Lab B, we take notes that utilize the F á a concept. Then we’re ready for the next unit,
which will introduce the concept of m ass.
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INQUIRY PHYSICS
A Modified Learning Cycle Curriculum
by Granger Meador
Unit 5:
Force and Acceleration
Student Papers
©2010 by Granger Meador
inquiryphysics.org
5 Force and Acceleration
Nam e
Lab A: Acceleration Due to a Constant Unbalanced Force
AIR TRACK VERSION
An automobile accelerates through an intersection after stopping at a stop sign only to accelerate negatively again to stop
at the next stop sign. An apple, being released from a tree, accelerates until it hits the ground. A baseball accelerates
from rest at the back of the pitcher's throw until it has a velocity of about 90 miles per hour toward the batter. How are
these events related? W hat causes the accelerations described? W hat variables are involved in producing the
acceleration of an object? How are these variables related? These questions make up the goal of the next series of labs.
You will be measuring the acceleration of gliders on an airtrack. The primary advantage of such a system is its very low
friction. This allows us to almost ignore frictional effects and concentrate on the interrelationships of force, acceleration,
and distance.
Purpose
The purpose of this lab is to determine how the acceleration of an object changes when a constant, unbalanced force
is applied over varying distances.
Air Track Guidelines
1.
Never move gliders along the air track when the air supply is shut off.
2.
Always be careful not to drop or damage the gliders - if one is bent, it will no longer function properly.
3.
All of the equipment in this lab is quite expensive, so be extra careful and conscientious.
Procedure
In this experiment you will use an air track, a
glider, a hanging weight holder with string, and
a stopwatch. The hanging weight provides an
unbalanced force, because there is no other
force balancing its pull on the glider.
A. Turn on the airtrack and check that the air
track is level by using one of the gliders. If
the glider does not remain fairly motionless
on the track, but tends to accelerate one way
or the other, ask your teacher to help you level the track.
B. Determine the acceleration of the glider over a distance of 0.900 meter, making at least three measurements of the
time it takes the glider to start from rest (v i=0) and travel the 0.900 meter. Use the built-in meter scale to determine
where the glider should be placed. Record the times in the table, making certain that all recorded times vary by no
more than 0.1 s. Average those measurements.
C. Repeat the above procedure for the remaining distances.
D. Use one of the motion equations to find the average acceleration of the cart for each distance.
Distance
(m)
Time (s)
Average Time (s)
Group's Average
Acceleration (m/s 2)
Class Average
Acceleration (m/s 2)
0.900
0.800
0.700
0.600
Unit 5: Force and Acceleration, Lab A: Acceleration Due to a Constant Unbalanced Force
© 2010 by G. Meador – www.inquiryphysics.org
Interpretation answer non-quantitative questions in complete sentences
1.
Show the motion equation you used to calculate acceleration:
2.
Plot the data points for your group’s data to help you see the relationship, if any, between the changing distance and the
calculated acceleration. Plot the independent variable on the x-axis and the dependent variable on the y-axis. Force each
axis to begin at zero.
Notice the difference between this graph and the two graphs you generated from the data in lab 1 (the ball rolling down
the ramp). Save your graph and show it to your teacher, but do not print it out unless directed to do so.
3.
One way to quantify how much change there is in a variable is to calculate the percentage difference. The formula is
shown below. W hat is the percentage difference if some arbitrary independent variable doubles? (Make up some
numbers and plug them into the formula; you need not use lab data here.)
4.
Consider a hypothetical linear graph, or directly proportional relationship. If you doubled the
independent variable, the dependent variable should also double. So if you had a directly
proportional relationship and the independent variable doubled, what percentage difference
would you expect to see for the dependent variable?
5.
For directly proportional relationships, tripling the independent variable triples the dependent, and so forth. Thus we
can generalize the concept from questions 3 and 4. W hen there is a directly proportional relationship, what should one
expect when comparing the percentage difference of the independent variable to that of the dependent variable?
6.
You will need the class average accelerations to answer questions 6-9. Quantify how much change there was in the
class average accelerations by calculating the percentage difference between the highest and lowest class average values.
(W e cannot calculate percentage error in this situation, as we do not know the theoretical values.) Show your work:
7.
To help you put this in perspective, calculate the percentage difference between the highest and lowest distances. Show
your work:
8.
Bear in mind your answer to question 5. Does the class data indicate a directly proportional relationship between
acceleration and distance? Explain why or why not.
9.
After considering a graph of the class data and the answers to questions 6-8, precisely describe what an object does when
a constant, unbalanced force is applied to it.
10.
W hat are the significant sources of systematic error in this experiment?
Unit 5: Force and Acceleration, Lab A: Acceleration Due to a Constant Unbalanced Force
© 2010 by G. Meador – www.inquiryphysics.org
5 Force and Acceleration
Lab A: Acceleration Due to a Constant Unbalanced Force
Nam e
DYNAMICS CART ON FLOOR VERSION
An automobile accelerates through an intersection after stopping at a stop sign only to accelerate negatively again to stop at the
next stop sign. An apple, being released from a tree, accelerates until it hits the ground. A baseball accelerates from rest at the
back of the pitcher's throw until it has a velocity of about 90 miles per hour toward the batter. How are these events related? W hat
causes the accelerations described? W hat variables are involved in producing the acceleration of an object? How are these
variables related? These questions make up the goal of the next series of labs.
The purpose of this lab is to determine how the acceleration of a cart changes when a constant force is applied. You should also
find out what effect changing the distance makes on the acceleration you measure.
Your teacher will explain the apparatus you will use. To get your apparatus ready for use, attach the long spring to the one end
of the meterstick with masking tape. Check that the spring scale has been zeroed and then hook the scale onto the other end of
the spring as shown in the drawing below.
You will need to determine the distance the spring has to stretch to give you a force of 2.00 N. You will need to put masking tape
on your meterstick to mark the stretch that will provide the force you need. After marking the meterstick, you will no longer need
to use the scale unless the long spring falls off the meterstick. If it ever does, always check that the 2.00 N mark has not been
changed by re-attaching the spring.
Exploration
Add one kilogram weights to your cart until the total weight of the cart (including the weight of the cart itself) is six kilograms.
Remove the scale from the spring and attach the free end of the spring (the other end should still be attached to the meterstick)
to the front of the cart and find a way to consistently make 2.00 N of force accelerate the cart. Practice accelerating the cart with
a constant force of 2.00 N over a distance of 1.500 m. That force is not balanced by anything and is, therefore, called an
unbalanced force.
A.
B.
C.
D.
E.
To determine the acceleration of the six kilogram cart over a distance of 1.500 meter, make at least three measurements
of the time it takes the cart to start from rest (v i=0) and travel the 1.500 meters. Record the times in the table, making
certain that all recorded times vary by no more than 1/10 s. Now average those measurements.
Repeat the above procedure, but this time determine the time the cart takes to travel a distance of 1.000 meter. Record
your data in the table.
Change the distance to .500 meters and repeat the procedure. Record your data in the table.
Use one of the motion equations to find the average acceleration of the cart for each distance.
The class averages will be calculated later and entered in the table.
Distance (m)
Time (s)
Average Time (s)
GROUP Average
Acceleration (m/s²)
CLASS Average
Acceleration (m/s 2)
1.500
1.000
.500
Unit 5: Force and Acceleration, Lab A: Acceleration Due to a Constant Unbalanced Force
© 2010 by G. Meador – www.inquiryphysics.org
The Idea
1.
W hich equation did you use to calculate acceleration?
2.
How do the average accelerations compare to each other?
W ait until the class has shared data, calculated class average accelerations, and discussed the results. Then
answer the following questions, basing your answers on the analysis of the overall class data.
3.
W e can give a quantitative answer to question 2 by calculating the percentage difference between the highest
and lowest values for the class' average accelerations. (W e cannot calculate percentage error in this situation,
as we do not know the theoretical values.) Show your work:
4.
To help you put this in perspective, calculate the percentage difference between the highest and lowest
distances. Show your work:
5.
Obviously, we changed the distance quite a bit to see what effect, if any, it would have on the acceleration of
a body which is being acted upon by a constant, unbalanced force. How much or what kind of effect did it
have?
6.
Precisely describe what an object does when a constant, unbalanced force is applied to it.
7.
W hat are the significant sources of systematic error in this experiment?
Unit 5: Force and Acceleration, Lab A: Acceleration Due to a Constant Unbalanced Force
© 2010 by G. Meador – www.inquiryphysics.org
5 Force and Acceleration
Lab A: Acceleration Due to a Constant Unbalanced Force
Nam e
DYNAMICS CART AND TABLE PULLEY VERSION
An automobile accelerates through an intersection after stopping at a stop sign only to accelerate negatively again to stop at the
next stop sign. An apple, being released from a tree, accelerates until it hits the ground. A baseball accelerates from rest at the
back of the pitcher's throw until it has a velocity of about 90 miles per hour toward the batter. How are these events related? W hat
causes the accelerations described? W hat variables are involved in producing the acceleration of an object? How are these
variables related? These questions make up the goal of the next series of labs.
The purpose of this lab is to determine how the acceleration of a cart changes when a constant force is applied. You should also
find out what effect changing the distance makes on the acceleration you measure.
Procedure
In this experiment you will use a rolling dynamics cart, table pulley, a hanging weight holder with string, and a stopwatch. The
hanging weight provides an unbalanced force, because there is no other force counteracting it.
Add one kilogram weights to your cart until the total weight of the cart (including the weight of the cart itself) is six kilograms.
Find a smooth and level part of the table or countertop where you can roll the cart horizontally over a large distance. M ount the
table pulley at the end of the run, and carefully measure and mark off the distances from the pulley which your teacher directs you
to use.
A.
B.
C.
D.
Determine the acceleration of the glider over the full distance, making at least three measurements of the time it takes
the glider to start from rest (v i=0) and travel the distance. Record the times in the table, making certain that all recorded
times vary by no more than 0.1 s. Average those measurements.
Collect the data for the remaining, shorter distances.
Use one of the motion equations to find the average acceleration of the cart for each distance.
The class averages will be calculated later and entered in the table.
Distance (m)
Time (s)
Average Time (s)
Unit 5: Force and Acceleration, Lab A: Acceleration Due to a Constant Unbalanced Force
GROUP Average
Acceleration (m/s²)
CLASS Average
Acceleration (m/s 2)
© 2010 by G. Meador – www.inquiryphysics.org
The Idea
1.
W hich equation did you use to calculate acceleration?
2.
How do the average accelerations compare to each other?
W ait until the class has shared data, calculated class average accelerations, and discussed the results. Then
answer the following questions, basing your answers on the analysis of the overall class data.
3.
W e can give a quantitative answer to question 2 by calculating the percentage difference between the highest and
lowest values for the class' average accelerations. (W e cannot calculate percentage error in this situation, as we
do not know the theoretical values.) Show your work:
4.
To help you put this in perspective, calculate the percentage difference between the highest and lowest distances.
Show your work:
5.
Obviously, we changed the distance quite a bit to see what effect, if any, it would have on the acceleration of a body
which is being acted upon by a constant, unbalanced force. How much or what kind of effect did it have?
6.
Precisely describe what an object does when a constant, unbalanced force is applied to it.
7.
W hat are the significant sources of systematic error in this experiment?
Unit 5: Force and Acceleration, Lab A: Acceleration Due to a Constant Unbalanced Force
© 2010 by G. Meador – www.inquiryphysics.org
5 Force and Acceleration
Nam e
W orksheet: Concepts & Calculations
answer in complete sentences
1.
How can you determine by watching a body whether or not an unbalanced force is acting on
it?
2.
Joe made a toy rocket-powered car. He wanted to measure the average acceleration of the
car. To do that, he timed the car over a distance of 0.500 m. He found that the car, starting
from rest, passed the 0.500 m mark so rapidly that he could not accurately measure the time.
Joe's friend Jack suggested that he increase the distance until the time became measurable.
Joe said that changing the distance would change the measurement of the acceleration, even
though the car was still moving under full power. If you were there, how would you respond
to the argument?
3.
Joe found that his car traveled 2.00 meters in 0.900 seconds.
acceleration?
4.
Assuming the acceleration of the car does not change, find the time required for the car to
to 4.00 meters starting from rest.
5.
Assuming the acceleration and weight of the car do not change, how does the force acting
on the car change as time and distance increase?
Unit 5: Force and Acceleration, Worksheet: Concepts & Calculations
What was the car's
© 2010 by G. Meador – www.inquiryphysics.org
5 Force and Acceleration
Nam e
Lab B: Varying Forces and Acceleration
AIRTRACK VERSION
The first lab with the air tracks showed that a constant unbalanced force creates a constant acceleration. The goal of this
experiment is to determine if the acceleration changes when the force acting on the object is varied, and if so what the precise
mathematical relationship is between the two variables.
Use the airtrack and glider system as before, but use two red gliders hooked together with velcro. Float each glider separately and
then let them gently link up. Use a conveniently large distance to make your timing measurements as easy as possible.
1.
Does every group have to use the same distance to compare their results? Explain why or why not.
use complete sentences
2.
Measure your hanging weight holder on the precision balance. Record the reading below:
W eight holder is
3.
grams.
W e need to convert the reading into the metric unit of weight, newtons. (The abbreviation for newtons is "N".) Multiply
the reading by 0.0098 to convert grams to newtons. Show the new value in the space below:
W eight holder weighs
N.
Using only the weight holder as the force on the glider, make three measurements of the time required to accelerate the glider from
rest to the end of the track. Record the distance traveled and the time elapsed in the table. Then gather data concerning the time
and distance when the force is increased by adding weights until the table is complete. (Don't forget to include the weight of the
weight holder on each run.)
Force (N)
4.
Distance
(m)
Time (s)
Avg. Time (s)
Avg. Accel.
(m/s 2)
Calculate the average time and acceleration of the glider for each run. How did increasing the force affect acceleration?
use complete sentences
Unit 5: Force and Acceleration, Lab B: Varying Forces and Acceleration
© 2010 by G. Meador – www.inquiryphysics.org
Your group will now plot your data with the computer. Plot the independent variable on the x-axis and the dependent variable
on the y-axis. Consider if it is logical to include (0,0) as a data point.
W hen you have plotted your data, ask your teacher to approve it before it is printed and saved.
answer in complete sentences
5.
W hy is (0,0) a valid data point on your graph? (No, it is NOT because the objects started from rest.)
6.
The shape of your graph indicates a specific mathematical relationship between force and acceleration. Describe that
relationship using the terminology you learned in earlier labs.
7.
The mathematical relationship you have described should allow you to predict how acceleration will change when force
changes. For example, if the force acting on an object doubles, what does your graph predict will happen to the
acceleration of the object?
8.
You should recall that the equation of a line is y=mx+b where m is the slope and b is the y-intercept. Your graph shows
the mathematical relationship between force and acceleration. W rite the complete equation for your graph, using F as
the symbol for force and a for acceleration and your graph's slope and y-intercept (properly rounded).
class’ average equation:
9.
Let's test your answer to question 3 by checking the acceleration when the force doubles. Use your graph’s equation to
find the theoretical acceleration at 0.200 N and 0.400 N of force. W rite down those values and then compare them
mathematically in a ratio. (Divide the larger acceleration value by the smaller one.) W rite your ratio down too, with
3 significant figures.
Accel. at 0.200 N =
m/s2
Accel. at 0.400 N =
m/s2
Accel. Ratio =
to 1
10.
Theoretically, what should the ratio be between the two accelerations? (Use your answer to question 3 to help you
answer this question. Notice the ratio of the forces we arbitrarily used in question 9.)
11.
W rite a brief conclusion stating what general principle or concept this lab has illustrated.
Unit 5: Force and Acceleration, Lab B: Varying Forces and Acceleration
© 2010 by G. Meador – www.inquiryphysics.org
5 Force and Acceleration
Nam e
Lab B: Varying Forces and Acceleration
DYNAMICS CART ON FLOOR VERSION
Everyone knows that the acceleration of a cart will increase if the force acting on the cart increases, providing all other factors
remain the same. The goal of this experiment is to determine how much the acceleration changes when the force acting on the
cart is changed by a definite amount. For example, we determined the acceleration of a 6 kilogram cart when a 2.00 newton
horizontal force was acting on it. How will the acceleration change if we double the horizontal force acting on the cart?
As you did in the previous experiment, mark the meterstick with masking tape. Mark it to know the length the spring has to stretch
to provide accelerating forces of 1.00 N, 2.00 N, 2.50 N, 3.00 N, 3.50 N, and 4.00 N.
On a level surface, measure and mark a distance of 1.00 meter (use masking tape). The weight of the cart should still be
6.00 kilograms.
A.
Using a horizontal force of 1.00 N, make three measurements of the time required to accelerate the cart from rest through
the distance of 1.00 meter. Record the distance and times in the table.
B.
Gather data concerning the time and distance when the horizontal force is 1.00 N, then 2.00 N, 2.50 N, 3.00 N, 3.50 N,
and 4.00 N. Record all data in the table. If the time measurement becomes less than 1.00 second, increase the
distance to 1.50 meters and continue.
Force (N)
Distance (m)
Time (s)
Avg. Time (s)
Avg. Accel. (m/s²)
1.00
2.00
2.50
3.00
3.50
4.00
Calculate the average time and acceleration of the glider for each run. How did increasing the force affect acceleration?
Unit 5: Force and Acceleration, Lab B: Varying Forces and Acceleration
© 2010 by G. Meador – www.inquiryphysics.org
Data will be combined from all laboratory groups in your class in order to make a class graph on the
computer. Graph acceleration in (m/s)/s on the vertical or "y" axis and force in newtons on the horizontal
or "x" axis. Force is on the x axis because it was the independent variable; the one you directly changed.
Acceleration is on the y axis because it was the dependent variable; its value depended on the force that
was applied. Include (0,0) as a data point. W hen you have plotted your data, ask your teacher to
approve it before it is printed and saved.
answer in complete sentences
1.
W hy is (0,0) a valid data point on your graph?
2.
The shape of your graph indicates a specific mathematical relationship between force and acceleration. Describe that
relationship using the terminology you learned in earlier labs.
3.
The mathematical relationship you have described should allow you to predict how acceleration will change when force
changes. For example, if the force acting on an object doubles, what does your graph predict will happen to the
acceleration of the object?
4.
You should recall that the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Your graph
shows the mathematical relationship between force and acceleration. W rite the complete equation for your graph, using
F as the symbol for force and a for acceleration and your graph's slope and y-intercept (properly rounded).
class' average equation:
5.
Let's test your answer to question 3. Use your graph's equation to find the theoretical acceleration at 1.80 N and 3.60 N
of force. W rite down those values and then compare them mathematically in a ratio. (Divide the larger acceleration
value by the smaller one.) W rite your ratio down too, with 3 significant figures.
Accel. at 1.80 N =
m/s2
Accel. at 3.60 N =
m/s2
Ratio =
to 1
6.
Theoretically, what should the ratio be between the two accelerations? (Use your answer to question 3 to help you
answer this question. Notice how we changed the force.)
7.
W rite a brief conclusion stating what general principle or concept this lab has illustrated.
Unit 5: Force and Acceleration, Lab B: Varying Forces and Acceleration
© 2010 by G. Meador – www.inquiryphysics.org
5 Force and Acceleration
Nam e
DYNAMICS CART AND TABLE PULLEY VERSION
Lab B: Varying Forces and Acceleration
The first lab with the dynamics cart showed a constant unbalanced force caused a constant acceleration. The goal of this
experiment is to determine if the acceleration changes when the force acting on the object is varied, and if so what the precise
mathematical relationship is between the two variables.
Set up the equipment as before, but this time always use the longest distance possible to help minimize timing errors.
Does every group have to use the same distance to compare their results? W hy or why not?
Measure your hanging weight holder on the balance. Record the reading below:
W eight holder is
grams.
W e need to convert the reading into the metric unit of weight, newtons. (The abbreviation for newtons is "N".) Multiply the
reading by 0.0098 to convert grams to newtons. Show the new value in the space below:
W eight holder weighs
A.
B.
N.
Using only the weight holder as the force on the cart, make three measurements of the time required to accelerate the cart
from rest to the pulley. Record the distance traveled and the time elapsed in the table.
Gather data concerning the time and distance when the force is increased by known weights (e.g. steadily adding slotted
weights to the weight hanger). Record all data in the table.
Force (N)
Distance (m)
Time (s)
Avg. Time (s)
Avg. Accel. (m/s²)
Calculate the average time and acceleration of the glider for each run. How did increasing the force affect acceleration?
Unit 5: Force and Acceleration, Lab B: Varying Forces and Acceleration
© 2010 by G. Meador – www.inquiryphysics.org
Your teacher will indicate if you are to graph your own data, or a data set formed from the average of all of the laboratory groups
in your class. Graph acceleration in (m/s)/s on the vertical or "y" axis and force in newtons on the horizontal or "x" axis. Force
is on the x axis because it was the independent variable; the one you directly changed. Acceleration is on the y axis because it
was the dependent variable; its value depended on the force that was applied. Include (0,0) as a data point. W hen you have
plotted your data, ask your teacher to approve it before it is printed and saved.
answer in complete sentences
1.
W hy is (0,0) a valid data point on your graph?
2.
The shape of your graph indicates a specific mathematical relationship between force and acceleration. Describe that
relationship using the terminology you learned in earlier labs.
3.
The mathematical relationship you have described should allow you to predict how acceleration will change when force
changes. For example, if the force acting on an object doubles, what does your graph predict will happen to the
acceleration of the object?
4.
You should recall that the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Your graph
shows the mathematical relationship between force and acceleration. W rite the complete equation for your graph, using
F as the symbol for force and a for acceleration and your graph's slope and y-intercept (properly rounded).
5.
Let's test your answer to question 3. Use your graph's equation to find the theoretical acceleration at one level of force
and then at another level of force that is twice as large. W rite down those values and then compare them mathematically
in a ratio. (Divide the larger acceleration value by the smaller one.) W rite your ratio down too, with 3 significant figures.
Accel. at
N=
m/s2
Accel. at
N=
m/s2
Ratio =
to 1
6.
Theoretically, what should the ratio be between the two accelerations? (Use your answer to question 3 to help you
answer this question. Notice how you changed the force.)
7.
W rite a brief conclusion stating what general principle or concept this lab has illustrated.
Unit 5: Force and Acceleration, Lab B: Varying Forces and Acceleration
© 2010 by G. Meador – www.inquiryphysics.org
Unit 5: Force and Acceleration
Meador’s Inquiry Physics
Page 1 of 4
INQUIRY PHYSICS
A Modified Learning Cycle Curriculum
Unit 5:
Force and Acceleration
Sample Notes
I recommend that you always write out notes,
by hand, on the board for each class. That
allows you to control the pacing and focus,
rather than having students ignore you while
they simply copy down the content of a slide. It
also controls your pacing, so that you don’t race
ahead but instead focus on student
understanding.
Ask frequent questions of students to check
their grasp of the material, and call upon
students to provide the next step when working
examples.
©2010 by Granger Meador
inquiryphysics.org
Unit 5 focuses on how force is
directly proportional to
acceleration, while distance has
no effect on acceleration when
force is constant. We
deliberately avoid using mass in
this unit.
My rule for students is that if I write it on the
board, they must write it in their notes, and I
grade their notes each quarter and take off for
any units with incomplete notes or examples.
Trigonometry-Based Physics
(AP Physics B)
This unit is identical for both algebra and trigbased courses.
Unit 5: Force and Acceleration
Meador’s Inquiry Physics
Page 2 of 4
Sample Notes for Unit 5: Force and Acceleration
Unit 5: Force and Acceleration
In 5 Lab A we found that acceleration is constant, over any distance, so long as a constant and
unbalanced force is applied. In 5 Lab B we found that the amount of unbalanced force is
directly proportional to an object’s acceleration:
Example 5-1
A car starts from rest in a drag race. When a constant force F is applied, the car travels a distance d
in a time t.
I.
If the distance were doubled to 2d, what would be the resulting acceleration in terms of a?
A.
B.
The answer is
II.
C.
D.
E.
, because distance has no effect on acceleration when force is constant.
If the distance were still doubled to 2d, what would be the resulting time in terms of t?
A.
B.
C.
D.
E. t
To solve this, we must follow this procedure:
1. Identify an equation in which the variable being changed and the one of interest both
appear, but in which no other variables are changing.
2. Solve the equation, if needed, for the variable of interest.
3. Insert a coefficient for the changing variable that matches the situation.
4. Balance the equation by inserting the same NET coefficient on the other (left) side of the
equation.
5. Simplify the left side – it shows how the variable of interest will change.
APPLYING THIS:
1.
related a and t, with d not changing.
2. That equation is already solved for t.
3. Insert a “2” in front of d since distance doubled:
4. That inserted a 2 in the numerator of a radical, or a NET coefficient of
so we insert
the same coefficient on the left side to balance the equation:
5. Thus the answer is that t has changed to become
; answer
was correct.
Unit 5: Force and Acceleration
Meador’s Inquiry Physics
Page 3 of 4
This is a very common type of question on the AP Physics B test and worth the time of students in any
physics course. If students do not grasp what is going on, put in some values for d and a and rework the
example. Next we’ll reinforce this idea.
Example 5-1 CONTINUED
III.
If the distance were returned to the original value d, while the force were doubled to 2F,
what would be the resulting acceleration in terms of a?
A.
B.
The answer is
IV.
C.
D.
E.
, because force and acceleration are directly proportional.
If the distance were d but the force doubled to 2F, what would be the resulting time in terms
of t?
A.
1.
B.
C.
D.
E. t
related a and t, with d not changing.
2. That equation is already solved for t.
3. Insert a “2” in front of a since acceleration doubled:
4. That inserted a 2 in the denominator of a radical, or a NET coefficient of
so we insert
the same coefficient on the left side to balance the equation:
5. Thus the answer is that t has changed to become
; answer
was correct.
That may suffice for now, but there are still common problems with the method, such as a student using an
equation in which more than two variables are changing. I’ve thrown in a part V if you wish to explore this.
Unit 5: Force and Acceleration
Meador’s Inquiry Physics
Page 4 of 4
Example 5-1 CONTINUED
V.
If the distance were d but the force doubled to 2F, what would be the resulting final velocity
in terms of the original final velocity vf?
We could try
, but must be cautious since both a and t will be changing!
1.
2. That equation is already solved for vf.
3. Insert “2” in front of a since acceleration doubled, but also insert
in front of t (see
Part IV above):
4. That inserted a 2 and
, for a NET coefficient of
, so we insert the same
coefficient on the left side to balance the equation:
5. Thus the answer is that vf has changed to become
ALTERNATE SOLUTION:
Here is how you solve it without that level of complexity. Use an equation in which no time
is shown:
1.
2. Solve for vf:
3. Insert “2” in front of a since acceleration doubled:
4. That inserted a NET coefficient of , so we insert the same coefficient on the left side
to balance the equation:
5. Thus the answer is that vf has changed to become