Download Unit 4 Packet (Labs)

under-inflated
billiard balls
colliding
100%
basketball
bouncing
90%
30%
ELASTIC
0%
INELASTIC
inflated
proton colliding with
another proton
basketball
bouncing
Conservation Laws
AP Physics 1
Mr. Kuffer
Motion Detector
Force Sensor
Elastic cord
Check Your Understanding
Express your understanding of the concept and mathematics of momentum by
answering the following questions.
1
NOTES:
I. (6.1)Work, measured in Joules (J), is done only in the direction of the force
causing the displacement.
Work = Force x Displacement
W = F x d… well, W = F x s… (always in direction of force)
W = (F Cos Θ) s
??(‘s’ is the ‘customary’ symbol for displacement when discussing work)??
In the words of Mike Tomlin… “It is what it is”
II. (6.9) Work done by variable force, Simple Harmonic Motion (SHM), &
Elasticity
(ex: Drawing back a bowstring… compressing or stretching a spring)
-
The work done by a variable force in moving an object is equal to the area
under the curve of ‘ FCosΘ vs s ‘ graph.
III. (10.1-10.2) The ‘Ideal Spring’ & Hooke’s Law – and ideal spring behaves
according to Hooke’s Law as follows:
Fx = -kx
Where k is the spring constant and x is the displacement of the spring
2
IV. (10.3) Energy and Simple Harmonic Motion (SHM)
-
Elastic Potential Energy – energy stored when a ‘spring’ is compressed or
stretched.
B/c the spring is ideal… Fx = -kx
However, we know the force is variable… that is it changes in time…
B/c the spring force on x is linear (‘ideal’ spring), the magnitude of the
average force is just ½ the sum of the initial and final values…
Fx = ½ (kxi + kxf)
So…
Welastic = (Fx Cos Θ) x = ½ (kxi + kxf) (Cos 0°) (xi-xf)
Or
Welastic = ½ kxi2 - ½ kxf2
V. (6.2) Work-Energy Theorem
When Work is done… there is a change in Kinetic Energy (ΔKE)
W = KEf - KEi = ½ mvf2 – ½ mvi2
3
VI. (6.3) Gravitational Potential Energy (Work done by gravity)
Wgravity = (mg Cos0°) (Δh) = mg (Δh)
Wgravity = mghf - mghi
VII.
(6.4) Conservative vs Nonconservative Forces
-
-
-
A force is conservative when the work it does on a moving object is
independent of the path between the object’s initial and final positions.
(Gravitational force is a conservative force)
A force is conservative when it does no net work on an object moving
around a closed path, starting and ending at the same point… (ex: riding a
roller coaster in a complete loop)
A force is nonconservative if the work it does on an object moving
between two points depends on the path of the motion between the points.
(Kinetic friction force is one example of a nonconservative force… air
resistance being another nonconservative force)
o The concept of potential energy is not defined for a
nonconservative force.
Wnc = ΔPE + ΔKE
4
VIII.
(6.5) The Conservation of Mechanical Energy
ME = KE + PE
or
Wnc = Ef –Ei
Note: if there are no nonconservative forces then…
Ef = Ei
Energy of a Horizontally Launched Projectile…
IX. (6.6) Nonconservative Forces and the Work-Energy Theorem
(most moving objects, in reality, experience nonconservative forces… So,)
Wnc = Ef –Ei
&
Wnc = (½ mvf2 + mghf ) – (½ mvi2 + mghi)
X. (6.7) Power – Simply the rate at which Work is done.
P=W/t
(Measured in Joules/s… 1 J/s = 1 Watt)
5
XI. (7.1) Impulse-Momentum Theorem
FΔt = mΔv
XII.
(7.2) Conservation of Linear Momentum
- Internal forces – forces that the objects within the system exert on each
other
- External forces – Forces exerted on the objects by agents external to the
system
- Remember F12 = -F21
(action-reaction pair)
ρ1 + ρ2 = ρ1' + ρ2'
m1v1 + m2v2 = m1v1' + m2v2'
** It is important to realize that the total linear momentum may be conserved even when
the kinetic energies of the individual parts of a system change (example below)
XIII.
(7.3) Collisions in One Dimension
- Elastic Collision – Total KE before equals total KE after collision
- Inelastic Collision - Total KE before does NOT equal total KE after
collision. If the objects stick together, the collision is said to be completely
elastic
under-inflated
billiard balls
colliding
100%
basketball
bouncing
90%
ELASTIC
30%
inflated
proton colliding with
another proton
basketball
bouncing
0%
INELASTIC
6
XIV. (7.4) Collisions in Two Dimensions
XV.
(7.5) Center of Mass (Average location of total mass… abbreviated ‘cm’)
7
YOU ARE POWERFUL!
Lab Data Sheet
PART I: Stairwell Lab
Step height __________
# of steps __________
Vertical displacement (m) _________
My Mass (kg) ____________
My Weight (lbs) ____________
My Force (N) ____________
(1 lb = 4.45N)
Directions: Walk or run up the stairs from the first to third floor three times. Increase
your speed with each trial. Carry a stop watch with you to measure the time. SAFETY
FIRST!!! If you feel faint, sick, or weak, STOP!!
My Data
Trial 1
Trial 2
Trial 3
Average
Time (s)
Work (J)
Power (W)
Group Member
Mass (kg)*
Height of
stairs (m)
Avg Time
(s)
Avg Work
(J)
Avg Power
(W)
(you)
8
1. Calculate the work for both you and your group members. Show sample calcs for
your first trial in your lab notebook.
Trial 1 data.
2. Calculate the power for you and your group members. Show work for your first trial
in your lab notebook.
Trial 1 data.
Analysis: (lab notebook)
3. Which of you did more work? Why?
4. Without changing the height of the stairs, could you have done something so that
the person that did the least amount of work did more work? Explain.
5. Which of you had more power? Why?
6. Without changing the height of the stairs, could you have done something so that
the person who had the least amount of power had more power? Explain.
7. (a) Calculate your power in kilowatts.
(b) Calculate your work done in calories. (1000 calories = 4186 J)
Applications:
8.
Your local electric company charges approximately $0.103 for one kilowatt-hour.
Suppose you could climb the stairs continuously for one hour. How much would this
climb be worth? (1 J = 2.78x10-7 kWh)
9
PART II: Build-a- Meal
Instructions: Each student will construct a meal and then analyze how much of a certain
activity must be done in order to “burn off” the energy that was consumed in the meal.
The meal must represent a meal you would actually order. Additional side orders are
permitted.
Use your Nutritional Value Chart to find the number of Calories in each item. Fill in the
chart below, then show your calculations (lab notebook). You should show ALL work,
use units throughout the problem and use proper problem skills.
Useful Information:
1 Cal = 4,184 J
1,000 cal = 1 Cal
Your Restaurant: _______________
Total Calories: _________________
Your Meal:
Quantity
Item
Total # Calories
Total # Joules
10
PART III: Nutristrategy.com
In this section you are now going to use your energy to work.
Remember: work = energy and energy = work.
First, you are going to do push-ups. You will need to measure your arm’s length and
change your weight in lbs to your mass in kg. How many push-ups can you do? How
many would you have to do to ‘burn’ off ALL of your caloric intake (a.k.a. your meal)?
W=Fxd
W = (mass x g)(arm’s length in meters)
Show Calculations here:
Number of push-ups:
Now, choose at least THREE activities from the website
http://www.nutristrategy.com/activitylist4.htm. You must calculate how
long each activity is done so that at the end of your last activity there are ZERO Calories left from the
meal you consumed.
Activity #1_________________ How long?______________
Activity #2__________________How long?_______________
Activity #3__________________ How long?_______________
11
Reference: Figure B
A 1.0 kg box, initially at rest and a height of 30.0 m, begins sliding down a frictionless surface.
When it reaches the bottom it starts sliding across the horizontal surface, then has a totally inelastic
collision with a 2.0 kg box. They stick together and begin to slide off together. After leaving this surface,
the system is projected horizontally, from a vertical height of 5.0m.
A) Calculate the speed of the 1.0 kg box at the bottom of the hill (before striking M2).
B) Calculate the speed of the two boxes after they collide.
C) Calculate the speed that the system has when it leaves the surface without
becomes a projectile.
D) Calculate the horizontal range of this projectile.
friction and
Figure B:
M1
h = 30m
M1 = 1 kg
M2 = 2 kg
M2
y = 5m
x = ? m
12
Projectiles & Energy Conservation
Pre-Lab
Experimental (Method 1)
Projectile Method
Theoretical (Method 2)
Conservation of Energy Method
1. Launch car
- measure dx, dy, and h as discussed in
class.
2. Determine ‘t’ using projectile method
(using dy = Vyi t + ½ at2)
3. Using ‘t’, solve for Vx…
Vx = dx / t
4. Solve for Vy…
Vyf2 = Vyi2 + 2ad
5. Solve for Vtot, using vector analysis…
Pythagorean Theorum
6. Using Vtot, and the KE equation
determine the EXPERIMENTAL KE.
7. KE = the energy of the system
1. Determine total energy of the system
using the total mass, gravitational
acceleration, and initial height of the
projectile.
2. PE = mgh, where ‘h’ is the total height
of the projectile before the launch (htot = h
+ Δy as shown below).
3. Notice that the PE determined above is
converted into the KE the projectile
experiences throughout the “trip”. (PE =
KE)
4. THEORETICAL PE at the top is
ideally equal to KE at the bottom!
h
htot
dy
After solving
for the energy of
dx
the system
using both
method 1 & 2, determine the “energy loss” of the system! (theoretical minus
experimental).
Name _______________________ Period _______ Date ___________
13
CONSERVATION OF ENERGY LABORATORY
Purpose: The purpose of this lab is to apply the law of conservation of energy and the principle
governing projectile motion to determine the amount of energy lost to friction as a
matchbox car rolls down a ramp.
Background and Theory: There are several ways that the motion of objects can be analyzed.
One way is by using kinematic equations and the idea of independence of horizontal and
vertical components of the motion. Another way is by using the Law of Conservation of
Mechanical Energy. In this laboratory, both methods will be used in determining the
mechanical energy “lost” due to the dissipative force of friction. It is important to
remember that the energy is not actually gone; rather it is converted into some other
form.
When using the Law of Conservation of Mechanical Energy, conditions are
assumed to be ideal, with no dissipative forces involved. Realistically, however, as a car
rolls down a ramp, the force of friction does lead to a loss of mechanical energy. In
calculating the mechanical energy at the bottom of the ramp, the value will be higher than
it should be, since the force of friction has not been considered. By finding the actual
velocity at the bottom of the ramp using projectile motion methods, a more accurate
value of the energy can be obtained. The difference in the energy values of each method
gives a good indication of how much energy was “lost” to friction.
Materials: matchbox car, ramp, meter stick, tape
Procedure:
1. Set up the apparatus as demonstrated.
2. Measure the height (h) to the top of the track in reference to the table top.
3. Measure the height of the table (Δdy).
4. Set your matchbox car at the top of the ramp, launch it, and note its approximate
landing position on the floor.
5. Place a piece of carbon paper on top of a piece of notebook paper on the floor where
the car landed.
6. Measure the horizontal distance (Δx) from the point of launch at the end of the ramp
to the landing location of the car.
Data and Calculations:
h
htot
h
dy
dx2
14
Table 1: Raw Data
Trial
dy (m)
h (m)
htot (m)
1
2
3
“
“
“
“
“
“
Table 2: Calculated data
Method 1 (projectile motion)
Trial
1
2
3
Ave
m (kg)
“
“
Method 2 (PE = mgh = KE)
IN PRACTICE
Vx (m/s)
dx (m)
IN THEORY
Vy (m/s)
“
“
“
Vtot (m/s)
KE (1) (J)
PE (J)
KE (J)
“
“
0
0
0
0
Energy Loss
(J)
*Show one sample calculation for each variable of table 2 in lab notebook.
Analysis:
1. In which method of calculating kinetic energy should you reach a result that is closer
to the “actual” kinetic energy of the car? Why?
2. In which method of calculating kinetic energy will the answer be true only if there was
no friction or outside forces acting on the system?
3. In this lab, you calculated an energy loss. Where did this energy go? In what form
was it lost?
4. Explain the main idea behind this lab. Specifically: Why are we able to subtract the
kinetic energies from each method to find the energy lost to friction?
15
Energy of a Tossed Ball
When a juggler tosses a bean ball straight upward, the ball slows down until it reaches the
top of its path and then speeds up on its way back down. In terms of energy, when the
ball is released it has kinetic energy, KE. As it rises during its free-fall phase it slows
down, loses kinetic energy, and gains gravitational potential energy, PE. As it starts
down, still in free fall, the stored gravitational potential energy is converted back into
kinetic energy as the object falls.
If there is no work done by frictional forces, the total energy will remain constant. In this
experiment, we will see if this works out for the toss of a ball.
Motion Detector
No basket necessary, do not let
the ball hit the motion detector
In this experiment, we will study these energy changes using a Motion Detector.
OBJECTIVES

Measure the change in the kinetic and potential energies as a ball moves in free fall.
 See how the total energy of the ball changes during free fall.
MATERIALS
computer
Vernier computer interface
Logger Pro
Vernier Motion Detector
volleyball, basketball, or other similar,
fairly heavy ball
16
PRELIMINARY QUESTIONS
For each question, consider the free-fall portion of the motion of a ball tossed straight
upward, starting just as the ball is released to just before it is caught. Assume that there is
very little air resistance.
1. What form or forms of energy does the ball have while momentarily at rest at the top
of the path?
2. What form or forms of energy does the ball have while in motion near the bottom of
the path?
3. Sketch a graph of velocity vs. time for the ball.
4. Sketch a graph of kinetic energy vs. time for the ball.
5. Sketch a graph of potential energy vs. time for the ball.
6. If there are no frictional forces acting on the ball, how is the change in the ball’s
potential energy related to the change in kinetic energy?
PROCEDURE
1. Measure and record the mass of the ball you plan to use in this experiment.
2. Connect the Motion Detector to the DIG/SONIC 1 channel of the interface. Place the
Motion Detector on the floor and protect it by placing a wire basket over it.
3. Open the file “16 Energy of a Tossed Ball” from the Physics with Vernier folder.
4. Hold the ball directly above and about 1.0 m from the Motion Detector. In this step,
you will toss the ball straight upward above the Motion Detector and let it fall back
toward the Motion Detector. Have your partner click
to begin data collection.
Toss the ball straight up after you hear the Motion Detector begin to click. Use two
hands. Be sure to pull your hands away from the ball after it starts moving so they are
not picked up by the Motion Detector. Throw the ball so it reaches maximum height
of about 1.5 m above the Motion Detector. Verify that the position vs. time graph
corresponding to the free-fall motion is parabolic in shape, without spikes or flat
regions, before you continue. This step may require some practice. If necessary,
repeat the toss, until you get a good graph. When you have good data on the screen,
proceed to the Analysis section.
17
DATA TABLE
Mass of the ball
Position
Time
(s)
Height
(m)
(kg)
Velocity
(m/s)
PE
(J)
KE
(J)
TE
(J)
After release
Top of path
Before catch
ANALYSIS
1. Click on the Examine tool, , and move the mouse across the position or velocity
graphs of the motion of the ball to answer these questions.
a. Identify the portion of each graph where the ball had just left your hands and was
in free fall. Determine the height and velocity of the ball at this time. Enter your
values in your data table.
b. Identify the point on each graph where the ball was at the top of its path.
Determine the time, height, and velocity of the ball at this point. Enter your values
in your data table.
c. Find a time where the ball was moving downward, but a short time before it was
caught. Measure and record the height and velocity of the ball at that time.
d. For each of the three points in your data table, calculate the Potential Energy (PE),
Kinetic Energy (KE), and Total Energy (TE). Use the position of the Motion
Detector as the zero of your gravitational potential energy.
2. How well does this part of the experiment show conservation of energy? Explain.
3. Logger Pro can graph the ball’s kinetic energy according to KE = ½ mv2 if you
supply the ball’s mass. To do this, choose Column Options Kinetic Energy from the
Data menu. Click the Column Definition tab.You will see a dialog box containing an
approximate formula for calculating the KE of the ball. Edit the formula to reflect the
mass of the ball and click
.
4. Logger Pro can also calculate the ball’s potential energy according to PE = mgh.
Here m is the mass of the ball, g the free-fall acceleration, and h is the vertical height
of the ball measured from the position of the Motion Detector. As before, you will
need to supply the mass of the ball. To do this, choose Column Options Potential
Energy from the Data menu. Click the Column Definition tab. You will see a dialog
box containing an approximate formula for calculating the PE of the ball. Edit the
formula to reflect the mass of the ball and click
.
5. Go to the next page by clicking on the Next Page button,
.
18
6. Inspect your kinetic energy vs. time graph for the toss of the ball. Explain its shape.
7. Inspect your potential energy vs. time graph for the free-fall flight of the ball. Explain
its shape.
8. Record the two energy graphs by printing or sketching.
9. Compare your energy graphs predictions (from the Preliminary Questions) to the real
data for the ball toss.
10. Logger Pro will also calculate Total Energy, the sum of KE and PE, for plotting.
Record the graph by printing or sketching.
11. What do you conclude from this graph about the total energy of the ball as it moved
up and down in free fall? Does the total energy remain constant?
12. Should the total energy remain constant? Why?
13. If it does not, what sources of extra energy are there or where could the missing
energy have gone?
THOUGHT EXPERIMENTS (DO NOT PERFORM, JUST PREDICT)
1. What would change in this experiment if you used a very light ball, like a beach ball?
2. What would happen to your experimental results if you entered the wrong mass for
the ball in this experiment?
3. Predict what would happen in a similar experiment using a bouncing ball. To do this,
you would mount the Motion Detector high and pointed downward so it can follow
the ball through several bounces.
19
Work and Energy
Work is a measure of energy transfer. In the absence of friction, when positive work is
done on an object, there will be an increase in its kinetic or potential energy. In order to
do work on an object, it is necessary to apply a force along or against the direction of the
object’s motion. If the force is constant and parallel to the object’s path, work can be
calculated using
W  F d
where F is the constant force and d the displacement of the object. If the force is not
constant, we can still calculate the work using a graphical technique. If we divide the
overall displacement into short segments, s, the force is nearly constant during each
segment. The work done during that segment can be calculated using the previous
expression. The total work for the overall displacement is the sum of the work done over
each individual segment:
W   F (d )d
This sum can be determined graphically as the area under the plot of force vs. position.1
These equations for work can be easily evaluated using a Force Sensor and a Motion
Detector. In either case, the work-energy theorem relates the work done to the change in
energy as
W = PE + KE
where W is the work done, PE is the change in potential energy, and KE the change in
kinetic energy.
In this experiment you will investigate the relationship between work, potential energy,
and kinetic energy.
OBJECTIVES

Use a Motion Detector and a Force Sensor to measure the position and force on a
hanging mass, a spring, and a dynamics cart.
 Determine the work done on an object using a force vs. position graph.
 Use the Motion Detector to measure velocity and calculate kinetic energy.
 Compare the work done on a cart to its change of mechanical energy.
MATERIALS
computer
Vernier computer interface
Logger Pro
Vernier Motion Detector
Vernier Force Sensor
1
masses (200 g and 500 g)
spring with a low spring constant (10 N/m)
masking tape
wire basket (to protect Motion Detector)
rubber band, dynamics cart
s final
If you know calculus you may recognize this sum as leading to the integral W   F ( s ) ds .
sinitial
20
PRELIMINARY QUESTIONS
1. Lift a book from the floor to the table. Did you do work? To answer this question,
consider whether you applied a force parallel to the displacement of the book.
2. What was the average force acting on the book as it was lifted? Could you lift the
book with a constant force? Ignore the very beginning and end of the motion in
answering the question.
3. Holding one end still, stretch a rubber band. Did you do work on the rubber band? To
answer this question, consider whether you applied a force parallel to the
displacement of the moving end of the rubber band.
4. Is the force you apply constant when you stretch the rubber band? If not, at what
point in the stretch is the force the least. At what point is the force the greatest?
PROCEDURE
Part I Work When The Force Is Constant
In this part you will measure the work needed to lift an object straight upward at
constant speed. The force you apply will balance the weight of the object, and so is
constant. The work can be calculated using the displacement and the average force,
and also by finding the area under the force vs. position graph.
1. Connect the Motion Detector to DIG/SONIC 1 of the interface. Connect the Vernier
Force Sensor to Channel 1 of the interface. Set the range switch to 10 N.
2. Open the file “18a Work and Energy” from the Physics with Computers folder. Three
graphs will appear on the screen: position vs. time, force vs. time, and force vs.
position. Data will be collected for 5 s.
3. You may choose to calibrate the Force Sensor, or you can skip this step.
a. Choose Calibrate  CH1: Dual Range Force from the Experiment menu. Click
.
b. Remove all force from the Force Sensor. Enter a 0 (zero) in the Value 1 field. Hold
the sensor vertically with the hook downward and wait for the reading shown for
Reading 1 to stabilize. Click
. This defines the zero force condition.
c. Hang the 500 g mass from the Force Sensor. This applies a force of 4.9 N. Enter
4.9 in the Value 2 field, and after the reading shown for Reading 2 is stable, click
. Click
to close the calibration dialog.
4. Hold the Force Sensor with the hook pointing downward, but with no mass hanging
from it. Click
, select only the Force Sensor from the list, and click
to
set the Force Sensor to zero.
21
5. Hang a 200 g mass from the Force Sensor.
6. Place the Motion Detector on the floor, away
from table legs and other obstacles. Place a
wire basket over it as protection from falling
weights.
Dual-Range
Force Sensor
7. Hold the Force Sensor and mass about 0.5 m
above the Motion Detector. Click
to
begin data collection. Wait about 1.0 s after the
clicking sound starts, and then slowly raise the
Force Sensor and mass about 0.5 m straight
upward. Then hold the sensor and mass still
until the data collection stops at 5 s.
8. Examine the position vs. time and force vs.
time graphs by clicking the Examine button, .
Identify when the weight started to move
upward at a constant speed. Record this starting
time and height in the data table.
9. Examine the position vs. time and force vs.
time graphs and identify when the weight
stopped moving upward. Record this stopping
time and height in the data table.
Figure 1
10. Determine the average force exerted while you were lifting the mass. Do this by selecting the
portion of the force vs. time graph corresponding to the time you were lifting (refer to the
position graph to determine this time interval). Do not include the brief periods when the up
motion was starting and stopping. Click the Statistics button, , to calculate the average
force. Record the value in your data table.
11. On the force vs. position graph select the region corresponding to the upward motion of the
weight. (Click and hold the mouse button at the starting position, then drag the mouse to the
stopping position and release the button.) Click the Integrate button, , to determine the area
under the force vs. position curve during the lift. Record this area in the data table.
12. Save the graphs (optional).
Part II Work Done To Stretch A Spring
In Part II you will measure the work needed to stretch a spring. Unlike the force
needed to lift a mass, the force done in stretching a spring is not a constant. The work
can still be calculated using the area under the force vs. position graph.
13. Open the file “18b Work Done Spring” from the Physics with Computers folder
Three graphs will appear on the screen: position vs. time, force vs. time, and force vs.
position. Data will be collected for 5 seconds.
14. Attach one end of the spring to a rigid support. Attach the Force Sensor hook to the
other end. Rest the Force Sensor on the table with the spring extended but relaxed, so
that the spring applies no force to the Force Sensor.
22
15. Place the Motion Detector about one meter from the Force Sensor, along the line of the
spring. Be sure there are no nearby objects to interfere with the position measurement.
Motion Detector
Force Sensor
Dual-Range
Force Sensor
Figure 2
16. Using tape, mark the position of the leading edge of the Force Sensor on the table. The
starting point is when the spring is in a relaxed state. Hold the end of the Force Sensor that is
nearest the Motion Detector as shown in Figure 3. The Motion Detector will measure the
distance to your hand, not the Force Sensor. With the rest of your arm out of the way of the
Motion Detector beam, click
. On the dialog box that appears, make sure that both
sensors are highlighted, and click
. Logger Pro will now use a coordinate system
which is positive towards the Motion Detector with the origin at the Force Sensor.
Force Sensor
Motion
Detector
Figure 3
17. Click
to begin data collection. Within the limits of the spring, move the Force Sensor
and slowly stretch the spring about 30 to 50 cm over several seconds. Hold the sensor still
until data collection stops. Do not get any closer than 40 cm to the Motion Detector.
18. Examine the position vs. time and force vs. time graphs by clicking the Examine button, .
Identify the time when you started to pull on the spring. Record this starting time and position
in the data table.
19. Examine the position vs. time and force vs. time graphs and identify the time when you
stopped pulling on the spring. Record this stopping time and position in the data table.
20. Click the force vs. position graph, then click the Linear Fit button, , to determine the slope
of the force vs. position graph. The slope is the spring constant, k. Record the slope and
intercept in the data table.
21. The area under the force vs. position graph is the work done to stretch the spring. How does
the work depend on the amount of stretch? On the force vs. position graph select the region
corresponding to the first 10 cm stretch of the spring. (Click and hold the mouse button at the
starting position, then drag the mouse to 10 cm and release the button.) Click the Integrate
button, , to determine the area under the force vs. position curve during the stretch. Record
this area in the data table.
23
22. Now select the portion of the graph corresponding to the first 20 cm of stretch (twice the
stretch). Find the work done to stretch the spring 20 cm. Record the value in the data table.
23. Select the portion of the graph corresponding to the maximum stretch you achieved. Find the
work done to stretch the spring this far. Record the value in the data table.
24. Save the graphs (optional).
Part III Work Done To Accelerate A Cart
In Part III you will push on the cart with the Force Sensor, causing the cart to accelerate. The
Motion Detector allows you to measure the initial and final velocities; along with the Force
Sensor, you can measure the work you do on the cart to accelerate it.
25. Open the file “18c Work Done Cart”. Three graphs will appear on the screen: position vs.
time, force vs. time, and force vs. position. Data will be collected for 5 seconds.
26. Remove the spring and support. Determine the mass of the cart. Record in the data table.
27. Place the cart at rest about 1.5 m from the Motion Detector, ready to roll toward the detector.
28. Click
. Check to see that both sensors are highlighted in the Zero Sensors Calibration
box and click
. Logger Pro will now use a coordinate system which is positive
towards the Motion Detector with the origin at the cart, and a push on the Force Sensor is
positive.
29. Prepare to gently push the cart toward the Motion Detector using the Force Sensor. Hold the
Force Sensor so the force it applies to the cart is parallel to the sensitive axis of the sensor.
30. Click
to begin data collection. When you hear the Motion Detector begin clicking,
gently push the cart toward the detector using only the hook of the Force Sensor. The push
should last about half a second. Let the cart roll toward the Motion Detector, but catch it
before it strikes the detector.
31. Examine the position vs. time and force vs. time graphs by clicking the Examine button, .
Identify when you started to push the cart. Record this time and position in the data table.
32. Examine the position vs. time and force vs. time graphs and identify when you stopped
pushing the cart. Record this time and position in the data table.
33. Determine the velocity of the cart after the push. Use the slope of the position vs. time graph,
which should be a straight line after the push is complete. Record the slope in the data table.
34. From the force vs. position graph, determine the work you did to accelerate the cart. To do
this, select the region corresponding to the push (but no more). Click the Integrate button, ,
to measure the area under the curve. Record the value in the data table.
35. Save the graphs (optional).
24
DATA TABLE
Part I
Time (s)
Position (m)
Start Moving
Stop Moving
Average force(N)
Work done (J)
Integral (during lift): force vs. position
(N•m)
PE (J)
Part II
Time (s)
Position (m)
Start Pulling
Stop Pulling
Spring Constant (N/m)
Stretch
10 cm
20 cm
Maximum
Integral (during pull)
(N•m)
PE (J)
Part III
Time (s)
Position (m)
Start Pushing
Stop Pushing
Mass (kg)
Final velocity (m/s)
Integral during push (N•m)
KE of cart (J)
25
ANALYSIS
1. In Part I, the work you did lifting the mass did not change its kinetic energy. The
work then had to change the potential energy of the mass. Calculate the increase in
gravitational potential energy using the following equation. Compare this to the
average work for Part I, and to the area under the force vs. position graph:
PE = mgh
where h is the distance the mass was raised. Record your values in the data table.
Does the work done on the mass correspond to the change in gravitational potential
energy? Should it?
2. In Part II you did work to stretch the spring. The graph of force vs. position depends
on the particular spring you used, but for most springs will be a straight line. This
corresponds to Hooke’s law, or F = – kx, where F is the force applied by the spring
when it is stretched a distance x. k is the spring constant, measured in N/m. What is
the spring constant of the spring? From your graph, does the spring follow Hooke’s
law? Do you think that it would always follow Hooke’s law, no matter how far you
stretched it? Why is the slope of your graph positive, while Hooke’s law has a minus
sign?
3. The elastic potential energy stored by a spring is given by PE = ½ kx2, where x is the
distance. Compare the work you measured to stretch the spring to 10 cm, 20 cm, and
the maximum stretch to the stored potential energy predicted by this expression.
Should they be similar? Note: Use consistent units. Record your values in the data
table.
4. In Part III you did work to accelerate the cart. In this case the work went to changing
the kinetic energy. Since no spring was involved and the cart moved along a level
surface, there is no change in potential energy. How does the work you did compare2
to the change in kinetic energy? Here, since the initial velocity is zero, KE = ½ mv
where m is the total mass of the cart and any added weights, and v is the final
velocity. Record your values in the data table.
EXTENSIONS
1. Show that one N•m is equal to one J.
2. Start with a stretched spring and let the spring do work on the cart by accelerating it
toward the fixed point. Use the Motion Detector to determine the speed of the cart
when the spring reaches the relaxed position. Calculate the kinetic energy of the cart
at this point and compare it to the work measured in Part II. Discuss the results.
3. Repeat Part I, but vary the speed of your hand as you lift the mass. The force vs. time
graph should be irregular. Will the force vs. position graph change? Or will it
continue to correspond to mgh?
4. Repeat Part III, but start with the cart moving away from the detector. Pushing only
with the tip of the Force Sensor, gently stop the cart and send it back toward the
detector. Compare the work done on the cart to the change in kinetic energy, taking
into account the initial velocity of the cart.
26
Egg Drop Lab
Theory and Inquiry
I.
Explain the theory behind the egg drop lab
impulse = Ft = mv = 
 Explain where the equation above came from and how it helps
in constructing the egg drop apparatus.
II.
Choose an equation from your equation sheet that will allow you to
solve for the final velocity of your egg. Calculate the final velocity
of your egg.
 You have to measure a variable in order to solve for the final
velocity. What is the variable?
Scoring:
1. Complete all questions in lab notebook
2. Egg drop apparatus is constructed
3. Egg survives drop from 1st flight of bleachers
4. Egg survives drop from top of bleachers
Total:




10 pts
5 pts
5 pts
+5 pts
20 pts
must be able to easily place and remove egg in apparatus
may only use cardboard, drinking straws, paper, and non-padded tape
may not use any parachute apparatus
apparatus may not exceed an 8 inch cube or sphere in size

27
Momentum Lab
Preliminary Questions:
1. Momentum is “__________________________________________”
2. List three examples of objects with a large amount of momentum
Instructions:
1. Set up the lab as indicated (and shown below)
2. Set the carts into motion by activating the spring mechanism
3. Calculate their momenta at the two points on the track.
4. IN YOUR LAB NOTEBOOK… fill in all of the data table
5. REMEMBER… Trials 6-9 are done on a slightly inclined track
Photogates
Flag
Calculations:
Since you cut a flag for the cart that is 2.54 cm (0.0254 m)
wide, the velocity of the cart can be calculated in the following
manner…
V = ∆d/t
* Where ∆d is 0.0254 m and the time is given by the photogate
Analysis Questions:
1. The momentum should not be the same at both positions… Why?
2. What would you find if a third photogate was placed along the track?
28
Data at Position #1
Trial #
Horizontal
track
Incline in
track
Mass of
Cart (kg)
Extra
mass (kg)
Total
Mass (kg)
Time at
Position #1 (s)
Velocity at
Position #1 (m/s)
Momentum at
Position #1 (kg m/s)
1
2
3
4
5
6
7
8
9
Data at Position #2
Trial #
Horizontal
track
Incline in
track
Time at
Position #2 (s)
Velocity at
Position #2 (m/s)
Momentum at
Position #2 (kg m/s)
“Lost” / Gained
Momentum (kg m/s)
1
2
3
4
5
6
7
8
9
29
Explosion Lab
Investigating the Law of Conservation of Momentum
NAME:_____________________
m1V1 + m2V2 = m1V1' + m2V2'
Cart #1 (Cart moving to the left after explosion)
Trial #
Mass of
Cart (kg)
1
2
3
4
5
6
7
8
9
.5
.5
.5
.5
.5
.5
.5
.5
.5
Additional
Mass in Cart
(kg)
0
.1
.2
.3
.4
.5
.6
.7
.8
Total Mass
(kg)
Time Velocity Momentum
(s)
(m/s)
(kg m/s)
Cart #2 (Cart moving to the right after explosion)
Trial
#
1
2
3
4
5
6
7
8
9
Mass
of
Cart
(kg)
.5
.5
.5
.5
.5
.5
.5
.5
.5
Additional
Mass in
Cart (kg)
Total
Mass
(kg)
Time Velocity Momentum Difference in
(s)
(m/s)
(kg m/s)
Momentum of
Two Carts
(kg m/s)
0
0
.1
.2
.3
.4
.5
.6
.7
* Was there a difference in the momentum of the
two carts? If there was, why? If there wasn’t,
why not?
30
Momentum and Collisions
The collision of two carts on a track can be described in terms of momentum
conservation. If there is no net external force experienced by the system of two carts, then
we expect the total momentum of the system to be conserved. This is true regardless of
the force acting between the carts.
Collisions are classified as elastic (kinetic energy is conserved), inelastic (kinetic energy
is lost) or completely inelastic (the objects stick together after collision). In this
experiment you can observe most of these types of collisions and test for the conservation
of momentum and energy in each case.
OBJECTIVES

Observe collisions between two carts, testing for the conservation of momentum.
 Classify collisions as elastic, inelastic, or partially elastic.
MATERIALS
computers
Vernier computer interface
Logger Pro
two Vernier Motion Detectors
dynamics cart track
two low-friction dynamics carts with
magnetic and Velcro™ bumpers
PRELIMINARY QUESTIONS
1. Consider a head-on collision between two billiard balls. One is initially at rest and the
other moves toward it. Sketch a position vs. time graph for each ball, starting with
time before the collision and ending a short time afterward.
2. As you have drawn the graph, is momentum conserved in this collision?
PROCEDURE
1. Measure the masses of your carts and record them in your data table. Label the carts
as cart 1 and cart 2.
2. Set up the track so that it is horizontal. Test this by releasing a cart on the track from
rest. The cart should not move.
3. Practice creating gentle collisions by placing cart 2 at rest in the middle of the track,
and release cart 1 so it rolls toward the first cart, magnetic bumper toward magnetic
bumper. The carts should smoothly repel one another without physically touching.
4. Place a Motion Detector at each end of the track, allowing for the 0.4 m minimum
distance between detector and cart. Connect the Motion Detectors to the DIG/SONIC 1
and DIG/SONIC 2 channels of the interface.
5. Open the file “18 Momentum Coll” from the Physics with Vernier folder.
31
6. Click
to begin taking data. Repeat the collision you practiced above and use
the position graphs to verify that the Motion Detectors can track each cart properly
throughout the entire range of motion. You may need to adjust the position of one or
both of the Motion Detectors.
7. Place the two carts at rest in the middle of the track, with their Velcro bumpers
toward one another and in contact. Keep your hands clear of the carts and click
. Select both sensors and click
. This procedure will establish the same
coordinate system for both Motion Detectors. Verify that the zeroing was successful
by clicking
and allowing the still-linked carts to roll slowly across the track.
The graphs for each Motion Detector should be nearly the same. If not, repeat the
zeroing process.
Part I: Magnetic Bumpers
8. Reposition the carts so the magnetic bumpers are facing one another. Click
to
begin taking data and repeat the collision you practiced in Step 3. Make sure you keep
your hands out of the way of the Motion Detectors after you push the cart.
9. From the velocity graphs you can determine an average velocity before and after the
collision for each cart. To measure the average velocity during a time interval, drag
the cursor across the interval. Click the Statistics button
to read the average value.
Measure the average velocity for each cart, before and after collision, and enter the
four values in the data table. Delete the statistics box.
10. Repeat Step 9 as a second run with the magnetic bumpers, recording the velocities in
the data table.
Part II: Velcro Bumpers
11. Change the collision by turning the carts so the Velcro bumpers face one another. The
carts should stick together after collision. Practice making the new collision, again
starting with cart 2 at rest.
12. Click
to begin taking data and repeat the new collision. Using the procedure
in Step 9, measure and record the cart velocities in your data table.
13. Repeat the previous step as a second run with the Velcro bumpers.
Part III: Velcro to Magnetic Bumpers
14. Face the Velcro bumper on one cart to the magnetic bumper on the other. The carts
will not stick, but they will not smoothly bounce apart either. Practice this collision,
again starting with cart 2 at rest.
15. Click
to begin data collection and repeat the new collision. Using the
procedure in Step 9, measure and record the cart velocities in your data table.
16. Repeat the previous step as a second run with the Velcro to magnetic bumpers.
32
DATA TABLE
Mass of cart 1 (kg)
Run
number
Run
number
Mass of cart 2 (kg)
Velocity of
cart 1
before
collision
Velocity of
cart 2
before
collision
Velocity of
cart 1 after
collision
Velocity of
cart 2
after
collision
(m/s)
(m/s)
(m/s)
(m/s)
1
0
2
0
3
0
4
0
5
0
6
0
Momentum
of cart 1
before
collision
(kg•m/s)
Momentum
of cart 2
before
collision
(kg•m/s)
1
0
2
0
3
0
4
0
5
0
6
0
Momentum
of cart 1
after
collision
(kg•m/s)
90%
ELASTIC
proton colliding with
another proton
Total
momentum
before
collision
(kg•m/s)
Total
momentum
after
collision
(kg•m/s)
Ratio of
total
momentum
after/before
under-inflated
basketball
bouncing
billiard balls
colliding
100%
Momentum
of cart 2
after
collision
(kg•m/s)
30%
inflated
basketball
bouncing
0%
INELASTIC
33
In this lab, we will collide two collision carts together to determine if momentum is conserved in
all types of collisions. To do this, we will obviously need to measure the velocity and mass of
each cart both before and after the collision. The above diagram might help you keep things
straight.
ANALYSIS
1. Determine the momentum (mv) of each cart before the collision, after the collision,
and the total momentum before and after the collision. Calculate the ratio of the total
momentum after the collision to the total momentum before the collision. Enter the
values in your data table.
2. If the total momentum for a system is the same before and after the collision, we say
that momentum is conserved. If momentum were conserved, what would be the ratio
of the total momentum after the collision to the total momentum before the collision?
3. For your six runs, inspect the momentum ratios. Even if momentum is conserved for a
given collision, the measured values may not be exactly the same before and after due
to measurement uncertainty. The ratio should be close to one, however. Is momentum
conserved in your collisions?
4. Classify the three collision types as elastic, inelastic, or completely inelastic.
EXTENSIONS
1. Using a collision cart with a spring plunger, create a super-elastic collision; that is, a
collision where kinetic energy increases. The plunger spring should be compressed
and locked before the collision, but then released during the collision. Measure
momentum before and after the collision. Is momentum conserved in this case?
2. Using the magnetic bumpers, consider other combinations of cart mass by adding
weight to one cart. Is momentum conserved in these collisions?
3. Using the magnetic bumpers, consider other combinations of initial velocities. Begin
with having both carts moving toward one another initially. Is momentum conserved
in these collisions?
* Answer in Lab Notebook!!!
34
Impulse Momentum Theorem
The impulse-momentum theorem relates impulse, the average force applied to an object
times the length of time the force is applied, and the change in momentum of the object:
F t  mv f  mvi
Here we will only consider motion and forces along a single line. The average force, F ,
is the net force on the object, but in the case where one force dominates all others it is
sufficient to use only the large force in calculations and analysis.
For this experiment, a dynamics cart will roll along a level track. Its momentum will
change as it reaches the end of an initially slack elastic tether cord, much like a horizontal
bungee jump. The tether will stretch and apply an increasing force until the cart stops.
The cart then changes direction and the tether will soon go slack. The force applied by
the cord is measured by a Force Sensor. The cart velocity throughout the motion is
measured with a Motion Detector. Using Logger Pro to find the average force during a
time interval, you can test the impulse-momentum theorem.
Motion Detector
Force Sensor
Elastic cord
OBJECTIVES
* Measure a cart’s momentum change and compare to the impulse it receives.
* Compare average and peak forces in impulses.
MATERIALS
computer
Vernier computer
Logger Pro
Vernier Motion Detector
Vernier Force Sensor
dynamics cart and track
clamp
elastic cord
string
500 g mass
35
PRELIMINARY QUESTIONS
1. In a car collision, the driver’s body must change speed from a high value to zero.
This is true whether or not an airbag is used, so why use an airbag? How does it
reduce injuries?
2. You want to close an open door by throwing either a 400 g lump of clay or a 400
g rubber ball toward it. You can throw either object with the same speed, but they
are different in that the rubber ball bounces off the door while the clay just sticks
to the door. Which projectile will apply the larger impulse to the door and be
more likely to close it?
PROCEDURE
1. Measure the mass of your dynamics cart and record the value in the data table.
2. Connect the Motion Detector to DIG/SONIC 1 of the interface. Connect the Force
Sensor to Channel 1 of the interface. If your Force Sensor has a range switch, set it to
10 N.
3. Open the file “20 Impulse and Momentum” in the Physics with Computers folder.
Logger Pro will plot the cart’s position and velocity vs. time, as well as the force
applied by the Force Sensor vs. time.
4. Optional: Calibrate the Force Sensor.
a. Choose Calibrate  CH1: Dual Range Force from the Experiment menu. Click
.
b. Remove all force from the Force Sensor. Enter a 0 (zero) in the Reading 1 field.
Hold the sensor vertically with the hook downward and wait for the reading shown
for CH1 to stabilize. Click
. This defines the zero force condition.
c. Hang the 500 g mass from the sensor. This applies a force of 4.9 N. Enter 4.9 in
the Reading 2 field, and after the reading shown for CH1 is stable, click
.
Click
to close the calibration dialog.
5. Place the track on a level surface. Confirm that the track is level by placing the lowfriction cart on the track and releasing it from rest. It should not roll. If necessary,
adjust the track.
6. Attach the elastic cord to the cart and then the cord to the string. Tie the string to the
Force Sensor a short distance away. Choose a string length so that the cart can roll
freely with the cord slack for most of the track length, but be stopped by the cord
before it reaches the end of the track. Clamp the Force Sensor so that the string and
cord, when taut, are horizontal and in line with the cart’s motion.
7. Place the Motion Detector beyond the other end of the track so that the detector has a
clear view of the cart’s motion along the entire track length. When the cord is
stretched to maximum extension the cart should not be closer than 0.4 m to the
detector.
36
8. Click
Sensor.
, select Force Sensor from the list, and click
to zero the Force
9. Practice releasing the cart so it rolls toward the Motion Detector, bounces gently, and
returns to your hand. The Force Sensor must not shift and the cart must stay on the
track. Arrange the cord and string so that when they are slack they do not interfere
with the cart motion. You may need to guide the string by hand, but be sure that you
do not apply any force to the cart or Force Sensor. Keep your hands away from
between the cart and the Motion Detector.
10. Click
to take data; roll the cart and confirm that the Motion Detector detects
the cart throughout its travel. Inspect the force data. If the peak exceeds 10 N, then
the applied force is too large. Roll the cart with a lower initial speed. If the velocity
graph has a flat area when it crosses the time-axis, the Motion Detector was too close
and the run should be repeated.
11.
Once you have made a run with good position, velocity, and force graphs, analyze
your data. To test the impulse-momentum theorem, you need the velocity before and
after the impulse. Choose an interval corresponding to a time when the elastic was
initially relaxed, and the cart was moving at approximately constant speed away from
the Force Sensor. Drag the mouse pointer across this interval. Click the Statistics
button, , and read the average velocity. Record the value for the initial velocity in
your data table. In the same manner, choose an interval corresponding to a time when
the elastic was again relaxed, and the cart was moving at approximately constant
speed toward the
Force Sensor. Drag the mouse pointer across this interval. Click the statistics button and
read the average velocity. Record the value for the final velocity in your data table.
12. Now record the time interval of the impulse. There are two ways to do this. Use the
first method if you have studied calculus and the second if you have not.
* Method 1: Calculus tells us that the expression for the impulse is equivalent to the
integral of the force vs. time graph, or
t final
F t 
 F (t )dt
tinitial
On the force vs. time graph, drag across the impulse, capturing the entire period
when the force was non-zero. Find the area under the force vs. time graph by
clicking the integral button, . Record the value of the integral in the impulse
column of your data table.
* Method 2: On the force vs. time graph, drag across the impulse, capturing the entire
period when the force was non-zero. Find the average value of the force by clicking
the Statistics button, , and also read the length of the time interval over which
your average force is calculated. The number of points used in the average divided
by the data rate of 50 Hz gives the time interval t. Record the values in your data
table.
37
13. Perform a second trial by repeating Steps 10 – 12, record the information in your data
table.
14. Change the elastic material attached to the cart. Use a new material, or attach two
elastic bands side by side.
15. Repeat Steps 10 – 13, record the information in your data table.
DATA TABLE
Mass of cart
kg
Trial
Final
Velocity
vf
Initial
Velocity
vi
Average
Force
F
Duration
of Impulse
t
Impulse
Elastic 1
(m/s)
(m/s)
(N)
(s)
(Ns)
1
2
Elastic 2
1
2
Trial
Elastic 1
Impulse
Ft
(Ns)
Change in
momentum
(kgm /s) or (Ns)
% difference between Impulse
and Change in momentum
(Ns)
1
2
Elastic 2
1
2
38
ANALYSIS
1. From the mass of the cart and change in velocity, determine the change in momentum
as a result of the impulse. Make this calculation for each trial and enter the values in
the second data table.
2. If you used the average force (non-calculus) method, determine the impulse for each
trial from the average force and time interval values. Record these values in your data
table.
3. If the impulse-momentum theorem is correct, the change in momentum will equal the
impulse for each trial. Experimental measurement errors, along with friction and
shifting of the track or Force Sensor, will keep the two from being exactly the same.
One way to compare the two is to find their percentage difference. Divide the
difference between the two values by the average of the two, then multiply by 100%.
How close are your values, percentage-wise? Do your data support the impulsemomentum theorem?
4. Look at the shape of the last force vs. time graph. Is the peak value of the force
significantly different from the average force? Is there a way you could deliver the
same impulse with a much smaller force?
5. Revisit your answers to the Preliminary Questions in light of your work with the
impulse-momentum theorem.
6. When you use different elastic materials, what changes occurred in the shapes of the
graphs? Is there a correlation between the type of material and the shape?
7. When you used a stiffer or tighter elastic material, what effect did this have on the
duration of the impulse? What affect did this have on the maximum size of the force?
Can you develop a general rule from these observations?
EXTENSIONS
1. Try other elastic materials, doing the same experiment.
39
Momentum Weblab
Using the following link, complete the following questions;
http://media.pearsoncmg.com/bc/aw_young_physics_11/pt1a/Media/Momentum/Collisio
nsElasticity/Main.html
40
NOTES
41