SOTM LAB: P 3
I.
TEACHER NOTES & GUIDELINES
TITLE OF LAB -- Force on an Inclined Plane
DEVELOPERS OF LAB
Kevin McGee JD567
OVERVIEW OF LAB
DESCRIPTION
In this activity students will investigate the force experienced by a body tending to pull it
down an inclined plane and how that force varies as the angle of elevation varies.
CURRICULUM CONSIDERATIONS
This activity is intended to show that the weight of a body can be resolved into
perpendicular components. Students should have completed investigations into
combining vectors and also have an understanding of static equilibrium. Students would
have also been introduced to Newton’s second law of motion.
REAL WORLD APPLICATIONS
Students that ride a bicycle or ski know that they accelerate more quickly down a steep
hill than they do down a shallow incline. This activity will demonstrate why that occurs.
SAFETY CONSIDERATIONS
Since the dynamics cart has low friction wheels it should not be allowed to roll freely on
a lab table when not in use. Care should be exercised in the handling of all sensors and
computer equipment.
BACKGROUND INFORMATION
A. SCIENTIFIC VIEWPOINT
When an object is at rest on a horizontal surface forces still are acting on it: the
force the Earth exerts on it (weight) and the force the surface exerts (normal
force). These forces continue to act even when the object is on an inclined plane.
The weight vector can be resolved into a component into the plane-mg cos- and
one parallel and down the plane-mg sin.
B. COMMON MISCONCEPTIONS
1. The component of force down an inclined plane is directly proportional to the
angle and not the sine of the angle.
2. An object at rest on an incline has no forces acting on it.
3. The inclined plane exerts a force vertically upward on an object at rest on the
plane.
OBJECTIVES
After completing this activity students will be able to:
1. Sketch all vectors acting on an object at rest on an inclined plane.
2. Develop the relationship between the force down the plane and the angle the plane
makes with the horizontal.
3. Explain how the force sensor pulling up the plane is measuring the component of the
force down the plane.
EQUIPMENT/MATERIALS
PROVIDED BY SOTM
Laptop computer with 500 or 750 Pasco Interface
Dynamics cart
1.20 m track with end stop
50 N Pasco force sensor
pivot clamp and universal clamp
ring stand (on request)
PROVIDED LOCALLY
String
Meter stick and protractor
ADVANCE PREPARATION
It is helpful to have one complete set up of the equipment for students to model before
class begins. It would also be helpful if LCD screen were available to demonstrate the
Science Workshop software if this is the first time it is being used.
II. PRE-LAB
PRE-LAB EXERCISE TO
MISCONCEPTIONS
ELICIT STUDENTS’
PRIOR KNOWLEDGE AND
The teacher might set a block of wood on a horizontal surface and ask students to sketch the
forces acting on the block. Next, raise the plane to make a small angle with the horizontal so that
the block still remains at rest. Have students again sketch the forces acting on the block. Next,
place a ball at the top of the plane and ask students to predict what will happen when the ball is
released. Discuss reasons why the ball accelerates down the plane but the block remains at rest.
How are the forces on the ball different than the forces on the block?
Gradually increase the angle that the incline makes with the horizontal. Why does the block
eventually start to move down the plane? What type of movement does the block have once it
starts to move? Where does the force come from to cause this motion? Have students again
sketch the forces acting on the block. Discuss any differences that came about.
DISCUSSION OF PRECONCEPTIONS
1. Since the friction encountered by the block of wood is greater than the ball, the ball
has a net force acting on it. Newton’s second law states the ball will accelerate.
2. As the angle is increased the ball accelerates more rapidly. There must be a greater
net force acting on it. The block too will eventually accelerate once it is no longer in
equilibrium. This seems to mesh with a student’s experience going downhill on a
bicycle or on skis.
3. As the angle increases the force down the plane increases but it is not directly
proportional to the angle. It is directly proportional to the sine of the angle.
III. EXPLORATION OF SCIENTIFIC PRINCIPLE
& INTRODUCTION OF EXPERIMENTAL
PROTOCOL
PROBLEM
How does the component of force down an inclined plane change as the angle is gradually
increased?
EXPERIMENT AND TECHNICAL OPERATION OF EQUIPMENT
The teacher will run and describe the activity using the PASCO interface and force sensor.
Measure the weight of the dynamics cart using the force sensor. Be sure to tare the sensor before
using. Mount the force sensor using the universal clamp and rod at the end of the track that will
be elevated. Raise one end of the track in uniform increments using the swivel clamp and ring
stand and measure the force down the plane. Record the angle and the force.
The following questions could be posed:
1. What happens to the force down the plane as one end of the track is elevated?
2. Sketch the following graphs based on the recorded data:
a. Force versus angle
b. Force versus sine angle
c. Force versus cosine angle
3. Using laptop computers and Science Workshop have students plot the three
relationships above. Discuss these three graphs and decide which relationship produces
a direct proportion.
4. The sine of angle is equal to the ratio of the height of the raised end to the length of
the track. The cosine could be determined in a similar fashion using the length of the
projection of the track on the horizontal and the length of the track. These values
could be calculated using the calculator function of the program and the 'add a
column’ feature of Science Workshop.
5. Using sampling options and keyboard monitoring one could raise the high end of the
track in fixed increments and record the measured force directly into the Science
Workshop program.
Step by step procedures (optional)
1. Remove the single foot from the end of track using a hex key so that one end rests
flush on the table.
2. Raise one end of the track using a pivot clamp and ring stand about 10 cm above the
table top.
3. Connect the force sensor DIN plug into the analog channel. Click and drag the
sensor’s plug to the same channel and do the same for “table”.
4. Using the force sensor mounted vertically measure the weight of a dynamics cart. Be
sure to tare the force sensor before using.
5. Select sampling options and click on “keyboard.” Fill in “Height” and “cm” in the
parameter boxes.
6. On table screen click on “add a column” icon and then add “height” to the table.
7. Mount the force sensor using a universal clamp and rod to the raised end of the track.
Place the dynamics cart on the track and attach it to the force sensor using a piece of
light string. Be sure the string is parallel to the track when viewed from the side. If
not, adjust the height of the force sensor.
8. With the raised end 10 cm above the table, click on the record button and enter. This
will read the force down the plane and record the value in the table.
9. Raise the end of the track to 15 cm. Type “15 cm” for entry #2 and press enter. This
will now raise the height in 5 cm increments for the remainder of the lab.
10. Continue elevating the raised end of the track until 45 cm high.
11. Measure the entire length of the track in centimeters using a meter stick and use in
#12.
12. Click of the “calculator” function. Input “height” / length of track. Input calculation
“sine theta” and short name “angle.” Press enter.
13. Click on “add a column.” Go to calculations and click on “sine theta.” [One could
also use a protractor and calculator to find the sine and cosine of the angles.]
14. To remove the negative sign from the force column create a new column that is force
*–1. Call this column “-force”.
15. Go to Display menu and click on “new graph.” Set the parameters with “-force” on
the y axis and “sine theta” on the x axis.
16. Click on statistics function button and linear curve fit. Highlight the linear section of
the graph and determine the slope of the highlighted segment section of the graph.
This should be the weight of the cart.
17. Calculate a percent difference.
IV. ELABORATION OF SCIENTIFIC PRINCIPLE:
INQUIRY-BASED STUDENT INVESTIGATION
PROBLEM
How does the force measured by the sensor change as the angle of elevation is increased?
HYPOTHESIS OR PREDICTION
Knowing the weight of the cart could you predict the magnitude of the force down the plane for a
specific angle of elevation?
EXPERIMENTAL DESIGN
1. What are the variables that will be measured in this investigation?
2. How will these variables be measured with the equipment supplied?
3. List the safety precautions that must be observed.
4. Check with your instructor after you have answered these questions.
Checkpoint (Teacher checks students’ experimental design for feasibility.)
Check proposed procedure. Does the process check? Ask students to explain why they
selected this procedure? Are they changing too many variables at any one time?
PLAN FOR DATA COLLECTION & ANALYSIS
1. What type of data must be gathered to test your prediction?
2. How will the data be displayed?
3. What graphs will be needed to evaluate your hypothesis?
Checkpoint (Teacher checks students’ plan for feasibility.)
CONDUCTING THE EXPERIMENT
After your procedure and data format has been checked by your instructor, perform the
experiment.
Checkpoint (Teacher monitors students’ investigations in progress.)
ANALYSIS OF DATA
1. Does your data appear to be reasonable?
2. How many trials should be run in order to prove your prediction?
3. Are you using the correct units for each parameter?
4. Construct at least two different graphs from the data gathered?
5. Explain the significance of each graph.
Checkpoint (Teacher checks students’ analysis.)
DISCUSSION OF RESULTS
COMPARE
1. What factors affected the magnitude of force down the plane?
2. What was the force down the plane directly related to?
3. Was your original hypothesis correct?
4. Did you alter your data collection techniques to determine a measurable pattern?
PERSUADE
1. What have you concluded?
2. What evidence do you have that supports your conclusion?
3. Does your conclusion allow you to make an accurate prediction?
4. Did you test your conclusion on a new situation?
5. Is your conclusion consistent with your pre-lab observations?
RELATE
1. If the parking brake in your car is not functioning properly, what could you do to
insure that when parked on a downhill your car will not roll into the car in front of it?
2. Why is a roof with a shallow pitch more likely to present problems for a home owner
after a heavy snowfall?
3. What criteria do ski slope operators use when labeling different trails (bunny slope
versus triple black diamond.)?
4. If you were designing a roller coaster ride for an amusement park, what could you do –
based on this activity- to increase the “thrills” on the ride for the passengers?
V.
EVALUATION
POST-LAB SURVEY OF STUDENTS’ CONCEPTIONS
Have students retake the Pre-Lab Exercise. Compare pre-lab and post-lab responses.
TRADITIONAL
Give students a blank diagram with an object on an inclined plane. Have them sketch all
forces acting on the object.
Have students, for a given angle and weight, calculate the magnitude of the force down
the plane. They could then set up a similar model with the SOTM equipment and test
their answer.
Select five questions from previous NYS Physics Regents.
ALTERNATIVE
1. You are planning summer vacation that will take through the Rocky Mountains.
The maximum grade of a road on the Interstate Highway System is 15o.
You would like to install a trailer hitch on your car. They are rated by load pulling
capacity. The trailer you wish to pull weighs 5000 N and experiences a frictional force of
1000 N. A normal car can accelerate at 2 m/s 2. Based on your knowledge of Newton’s
second law and the results of this lab determine how much strain the hitch you purchase
should be able to withstand so that you will have a safe trip. List all assumptions made
and show all calculations with units.
2. Have students predict the angle the track must be elevated in order for a block to slide
down with constant speed after given a slight push. (This activity would be appropriate
for advanced students with a background in frictional coefficients.)
This material is based upon work supported by the National Science Foundation under Grant No. ESI 9618936. Any opinions,
findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the
views of the National Science Foundation.