unit 5: force and acceleration - bartlesville public · pdf fileinquiry physics...

INQUIRY PHYSICS inquiryphysics.orgA Modified Learning Cycle Curriculumby Granger Meador, ©2010

Unit 5: Force and Acceleration

Teacher’s Guide

Student Papers

Sample Notes

http://www.design-simulation.com/

5 Force and Acceleration Teacher's GuideInquiry 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, culminate in the students deriving the Newton's Second Law

of Motion (Law of Acceleration; F=ma). You will want to keep reminding the students of previous results

as you build toward that goal.

Throughout the labs in this unit, the mass concept is to be scrupulously avoided, so as not to short-circuit

concept development in the following unit. If a student mentions mass, do not go into that topic, and don't

be afraid to act as though kilograms is a unit of weight for now. In the next unit, the students will

conceptualize mass and the distinction between kilograms and newtons will be made. Also, many

students are not formal-operational and cannot accept that balances can measure mass even though they

are really measuring weight (because mg for one side equals mg for the other and the g will cancel out).

LAB A: Acceleration Due to a Constant Unbalanced Force

Exploration

Equipment 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

Dynamics cart on floor version:

dynamics cart (taping weights onto each cart beforehand

to make it a convenient weight can save lab time)

5 N and/or 20 N spring scale

meterstick

long spring (perhaps cut a worn-out wave demonstrator

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 thumbtack or small nail) to secure spring to meterstick

enough weights to bring loaded cart up to 6 kg

INQUIRY PHYSICS TEACHER 'S GUIDE FOR UNIT 5: FORCE AND ACCELERATION PAGE 2 OF 9

Dynamics cart and table pulley version:

dynamics cart (taping weights onto each cart beforehand to make it a

convenient weight can save lab time)

table pulley

string/fishing line


meterstick


If using air tracks, use a small hanging weight or the runs will be too fast for the stopwatches. You may

wish to use fancy timing equipment, but be careful not to allow fancy equipment to do the thinking for the

students; calculating accelerations from stopwatch readings is a useful approach since it is easily

igeneralized by students to all motions and reinforces the use of a = 2d/t when v =0. Leveling the track is2

crucial, as is not allowing the hanging weight to swing as it falls nor letting it reach the floor.

If using the dynamics carts on the floor, students may need help keeping the force constant as they

accelerate the cart. Observe them to ensure that they are keeping the spring stretched the same length

along the meterstick throughout the entire trip; they will have a tendency to slack off as the speed builds

and this can lead to large experimental 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 equipment and to

minimize error.

If using the dynamics carts with a table pulley, make sure your runs are long enough so that timing 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 measurements; 2) to let students

see what a "null result" looks like (they will usually struggle to interpret experimental error in this lab as

evidence of some relationship between d and a); and 3) for the dynamics cart version of the lab, this lab

provides experience in keeping the force constant through varied distances to improve their work in Lab B.

Supervise the completion 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 meticulous about how the table is completed.


The Idea

The analysis is more detailed in the air track version, as it provides more data points of greater accuracy

and precision than the other versions.

Lab A Sample Answers for AIR TRACK version

1. Show the motion equation you used to calculate acceleration: ? a = 2d / t2

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. What 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?

varies

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. When 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?

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. (We 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 thereis 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:


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 aconstant, unbalanced force is applied.

10. What are the significant sources of systematic error in this experiment?

Timing and friction are the major systematic errors.

Lab A Sample Answers for DYNAMICS CART versions (either on floor or with a table pulley)

1. W hich equation did you use to calculate acceleration? a = 2d / t2

2. How do the average accelerations compare?

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 shown a rough plot of d vs. a

to see that it is forming a fairly striaght line for the class as a whole; questions 3 and 4 will

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 much or

what kind of effect did it have?

Changing the distance did not affect the acceleration beyond a levelexplainable by experimental error.(This is because the time was 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.)


Expansion of the Idea - WORKSHEET

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 determine by watching a body whether or not an unbalanced force is acting on it?

It will accelerate.

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?

Joe is wrong; changing distance will not affect acceleration when force isconstant.

3. Joe found that his car traveled 2.00 meters in 0.900 seconds. W hat was the car's 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?

It does not change.


Expansion of the Idea - LAB B: VARYING FORCES AND ACCELERATION

Equipment 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 bumpers (or carefully brought together on an active air

track and secured with a paperclip)

stopwatch

string/fishing line


5 washers (or other small identically-sized weights)

Dynamics cart on floor version:

dynamics cart (taping weights onto each cart beforehand to make it a convenient weight can save

lab time)

5 N and/or 20 N spring scale

meterstick

long spring (perhaps cut a worn-out wave demonstrator spring to 50 cm; avoid Slinkies, which are

too large, and rubber bands, which don't have a constant force/stretch ratio)

tape (or thumbtack or small nail) to secure spring to meterstick


Dynamics cart and table pulley version:

dynamics cart (taping weights onto each cart beforehand to make it a convenient weight can save

lab time)

table pulley

string/fishing line


meterstick


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

timing errors will become 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 timing equipment, this lab is

better for that than Lab A.

If using dynamics carts on the floor, feel free to adjust the mass of the cart or the spring forces to suit your

equipment and reduce error. Emphasize the importance of keeping the force constant throughout the

entire run, especially on the runs with larger forces. Slacking off will create unacceptable experimental

error.

If using dynamics carts and table pulleys, feel free to adjust the mass of the cart and the amount of

hanging weight to match your equipment and reduce error.


Lab B Sample Answers for AIR TRACK version

1. Does every group have to use the same distance to compare 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, itwould 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 varies grams.

3. 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 varies N.

4. Calculate the average time 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 mathematical relationship between force and

acceleration. Describe that relationship using the terminology you learned in earlier labs.

They are directly proportional. (Do not accept “directly related”.)

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?

The acceleration will also double.

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).

a = mF+b (m will 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 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/s Accel. at 0.400 N = m/s Ratio = to 12 2

(answers will 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 thegraph, 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.


Lab B Sample Answers for DYNAMICS CART versions (either on floor or with 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 mathematical relationship between force and

acceleration. Describe that relationship using the terminology you learned in earlier labs.

It is a linear/directly proportional relationship.

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?

The acceleration will double.

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).

a = mF+b (m will be their graph's slope and b should be close to zero)

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/s Accel. at N = m/s Ratio = to 12 2

(answers will vary, but their ratio should come out close to 2 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.)

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 mass.


INQUIRY PHYSICSA Modified Learning Cycle Curriculumby Granger Meador

Unit 5:Force and Acceleration

Student Papers©2010 by Granger Meador

inquiryphysics.org

http://inquiryphysics.org

5 Force and Acceleration Name

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? What causes the accelerations described? What 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 Guidelines1. 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

itime it takes the glider to start from rest (v =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 thecalculated acceleration. Plot the independent variable on the x-axis and the dependent variable on the y-axis. Force eachaxis 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 downthe 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 isshown below. What is the percentage difference if some arbitrary independent variable doubles? (Make up somenumbers 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 theindependent variable, the dependent variable should also double. So if you had a directlyproportional relationship and the independent variable doubled, what percentage differencewould you expect to see for the dependent variable?

5. For directly proportional relationships, tripling the independent variable triples the dependent, and so forth. Thus wecan generalize the concept from questions 3 and 4. When there is a directly proportional relationship, what should oneexpect 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 theclass average accelerations by calculating the percentage difference between the highest and lowest class average values. (We 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. Showyour work:

8. Bear in mind your answer to question 5. Does the class data indicate a directly proportional relationship betweenacceleration 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 whena constant, unbalanced force is applied to it.




5 Force and Acceleration NameLab A: Acceleration Due to a Constant Unbalanced Force 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 thenext stop sign. An apple, being released from a tree, accelerates until it hits the ground. A baseball accelerates from rest at theback of the pitcher's throw until it has a velocity of about 90 miles per hour toward the batter. How are these events related? Whatcauses the accelerations described? What variables are involved in producing the acceleration of an object? How are thesevariables 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 alsofind 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 endof the meterstick with masking tape. Check that the spring scale has been zeroed and then hook the scale onto the other end ofthe 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 tapeon your meterstick to mark the stretch that will provide the force you need. After marking the meterstick, you will no longer needto 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 beenchanged by re-attaching the spring.

ExplorationAdd 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 witha constant force of 2.00 N over a distance of 1.500 m. That force is not balanced by anything and is, therefore, called anunbalanced force.

A. To determine the acceleration of the six kilogram cart over a distance of 1.500 meter, make at least three measurements

iof the time it takes the cart to start from rest (v =0) and travel the 1.500 meters. Record the times in the table, makingcertain that all recorded times vary by no more than 1/10 s. Now average those measurements.

B. Repeat the above procedure, but this time determine the time the cart takes to travel a distance of 1.000 meter. Recordyour data in the table.

C. Change the distance to .500 meters and repeat the procedure. Record your data in the table.D. Use one of the motion equations to find the average acceleration of the cart for each distance.E. The class averages will be calculated later and entered in the table.

Distance (m) Time (s) Average Time (s) GROUP AverageAcceleration (m/s²)

CLASS AverageAcceleration (m/s )2

1.500

1.000

.500



The Idea

1. Which equation did you use to calculate acceleration?

2. How do the average accelerations compare to each other?

Wait until the class has shared data, calculated class average accelerations, and discussed the results. Thenanswer the following questions, basing your answers on the analysis of the overall class data.

3. We can give a quantitative answer to question 2 by calculating the percentage difference between the highestand lowest values for the class' average accelerations. (We 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 lowestdistances. Show your work:

5. Obviously, we changed the distance quite a bit to see what effect, if any, it would have on the acceleration ofa body which is being acted upon by a constant, unbalanced force. How much or what kind of effect did ithave?





5 Force and Acceleration NameLab A: Acceleration Due to a Constant Unbalanced Force 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 thenext stop sign. An apple, being released from a tree, accelerates until it hits the ground. A baseball accelerates from rest at theback of the pitcher's throw until it has a velocity of about 90 miles per hour toward the batter. How are these events related? Whatcauses the accelerations described? What variables are involved in producing the acceleration of an object? How are thesevariables 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 alsofind out what effect changing the distance makes on the acceleration you measure.

ProcedureIn this experiment you will use a rolling dynamics cart, table pulley, a hanging weight holder with string, and a stopwatch. Thehanging 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. Mount thetable pulley at the end of the run, and carefully measure and mark off the distances from the pulley which your teacher directs youto use.

A. Determine the acceleration of the glider over the full distance, making at least three measurements of the time it takes

ithe glider to start from rest (v =0) and travel the distance. Record the times in the table, making certain that all recordedtimes vary by no more than 0.1 s. Average those measurements.

B. Collect the data for the remaining, shorter distances.C. Use one of the motion equations to find the average acceleration of the cart for each distance.D. The class averages will be calculated later and entered in the table.

Distance (m) Time (s) Average Time (s) GROUP AverageAcceleration (m/s²)

CLASS AverageAcceleration (m/s )2



The Idea

1. Which equation did you use to calculate acceleration?

2. How do the average accelerations compare to each other?

Wait until the class has shared data, calculated class average accelerations, and discussed the results. Thenanswer the following questions, basing your answers on the analysis of the overall class data.

3. We can give a quantitative answer to question 2 by calculating the percentage difference between the highest andlowest values for the class' average accelerations. (We cannot calculate percentage error in this situation, as wedo 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 bodywhich is being acted upon by a constant, unbalanced force. How much or what kind of effect did it have?






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 onit?

2. Joe made a toy rocket-powered car. He wanted to measure the average acceleration of thecar. To do that, he timed the car over a distance of 0.500 m. He found that the car, startingfrom 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, eventhough the car was still moving under full power. If you were there, how would you respondto the argument?

3. Joe found that his car traveled 2.00 meters in 0.900 seconds. What was the car'sacceleration?

4. Assuming the acceleration of the car does not change, find the time required for the car toto 4.00 meters starting from rest.

5. Assuming the acceleration and weight of the car do not change, how does the force actingon the car change as time and distance increase?

Unit 5: Force and Acceleration, Worksheet: Concepts & Calculations © 2010 by G. Meador – www.inquiryphysics.org



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:

Weight holder is grams.

3. We 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:

Weight 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)Distance

(m)Time (s) Avg. Time (s)

Avg. Accel.

(m/s )2

4. 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.

When you have plotted your data, ask your teacher to approve it before it is printed and saved.


5. Why 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. Write 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. Write down those values and then compare them

mathematically in a ratio. (Divide the larger acceleration value by the smaller one.) Write your ratio down too, with

3 significant figures.

Accel. at 0.200 N = m/s Accel. at 0.400 N = m/s Accel. Ratio = to 12 2

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. Write a brief conclusion stating what general principle or concept this lab has illustrated.




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?



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. When you have plotted your data, ask your teacher to

approve it before it is printed and saved.


1. Why is (0,0) a valid data point on your graph?






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. Write 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. Write down those values and then compare them mathematically in a ratio. (Divide the larger acceleration

value by the smaller one.) Write your ratio down too, with 3 significant figures.

Accel. at 1.80 N = m/s Accel. at 3.60 N = m/s Ratio = to 12 2


answer this question. Notice how we changed the force.)





Lab B: Varying Forces and Acceleration DYNAMICS CART AND TABLE PULLEY VERSION

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? Why or why not?

Measure your hanging weight holder on the balance. Record the reading below:

Weight holder is grams.

We 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:

Weight holder weighs N.

A. 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.

B. 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?



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. When you have

plotted your data, ask your teacher to approve it before it is printed and saved.


1. Why is (0,0) a valid data point on your graph?






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. Write 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. Write down those values and then compare them mathematically

in a ratio. (Divide the larger acceleration value by the smaller one.) Write your ratio down too, with 3 significant figures.

Accel. at N = m/s Accel. at N = m/s Ratio = to 12 2


answer this question. Notice how you changed the force.)




Unit 5: Force and Acceleration Meador’s Inquiry Physics Page 1 of 4

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.

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 trig-

based courses.

INQUIRY PHYSICS A Modified Learning Cycle Curriculum

Unit 5: Force and Acceleration Sample Notes ©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.

http://inquiryphysics.org/


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. C.

D. E.

The answer is , because distance has no effect on acceleration when force is constant.

II. 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.


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. C.

D. E.

The answer is , because force and acceleration are directly proportional.

IV. If the distance were d but the force doubled to 2F, what would be the resulting time in terms

of t?

A. B. C.

D. E. t

1.

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.


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

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