Lesson 3  Centripetal Force
Lesson Plan
Grade Level
High School
State Standards:
1. Motion and Forces
Central Concept: Newton's laws of motion and gravitation describe and predict the motion of most objects.
1.4 Interpret and apply Newton's three laws of motion.
1.8 Describe conceptually the forces involved in circular motion.
Essential Question:
How do Newton's laws of motion describe and predict the motion of objects?
Lesson Question:
How do objects move in circular paths?
Introduction:
In this lab you will study how objects move in circular paths. An object moving in a circle at constant speed is accelerating because the direction of the velocity is changing. Since the change in velocity is directed towards the center of the circle the acceleration is called centripetal acceleration. The force required to produce this acceleration is called the centripetal force. Any net force that causes an object to move in a circular path can be a centripetal force. The equation relating centripetal force, mass and velocity is Fc = mv2/r , where Fc is the centripetal force, m is the mass of the object, v is its velocity and r is the radius of the circle. In Part 1 of this lab you will vary the centripetal force and measure the change in the object's speed while holding the radius and mass constant. In part 2 of the lab you will vary the radius of revolution and determine the velocity holding force and mass constant. Finally the mass of the object revolving will be varied and you will hold the force and radius constant while determining velocity.
Task:
The purpose of this lab is for you to investigate the relationship between the speed of an object moving in uniform circular motion and the centripetal force acting on the object , the mass of the object and the radius of the circle. You will use an online simulator for centripetal motion or do a conventional centripetal force lab. To verify that Fc = mv2/r is the correct quantitative relationship between centripetal force, mass, velocity and radius, you will determine how velocity changes as a result of manipulating one of the other variables in the equation while holding the other two constant. It is difficult to manipulate velocity and so velocity will always be the dependent variable. You will create three graphs from your data and determine the slope of each graph which relate to the variables held constant. You will calculate the percent error between the actual values of the constants and their experimental values and answer discussion questions.
Lesson Experiences:
You will first recall the reason objects go in circular paths by clicking on the following link: circular motion
 To begin the lab click on the simulator link to run the simulator lab or click on the convectional lab link to obtain the Centripetal Force lab handout: simulator
 If simulator cannot be used then click on the following link: Centripetal Force Lab
 Follow the directions in simulator lab which are located in the left side of the screen.
In Part 1 you will vary the centripetal force on an object revolving in a circular path at a constant radius of revolution and determine the velocity of the object.
 Create a graph of Force centripetal verses v2
 The centripetal force should be directly proportional to the square of the speed.
 Draw the best smooth curve through your data points and determine the slope.
 Determine m/r.
 Divide the value of m by the value of r to determine the known value for m/r.
 Calculate and record the percent error: percent error.
 Experimental value (m/r)exp is the slope of the line which you will compare to the known value of m/r.
 Print out lab report.
 Answer the following questions.
 Is the graph of centripetal force versus speed squared a straight line?
 What is the relationship between force and speed?
In Part 2 you will vary the radius of revolution of an object revolving in a circular path at a constant value for the centripetal force and determine the velocity of the object.
 Follow directions in simulator for part 2
 Answer the following questions.
 Is the graph of speed squared verses radius a straight line?
 What is the relationship between speed squared and radius?
In Part 3 you will vary the mass of an object revolving in a circular path at constant values for the centripetal force and radius of revolution and determine the velocity of the object.
 Follow directions in simulator for Part 3.
 Answer the following questions:
 Is the graph of velocity squared versus 1/m a straight line?
 What is the relationship between velocity and mass?
Conclusion:
In this lab you have verified the quantitative relationships between centripetal forces, mass, velocity and radius of an object moving at constant velocity in circular motion. You now have an understanding of what will happen if one of the variables in the equation changes and how another responds to that change provided the other two variables are held constant. By graphing the data you are able see mathematically the relationship between the variables.
Assessments:
You will be able to.... 
Strong 
Good 
Adequate 
Inadequate 
% 
Graph data collected in lab 
Graph contains title and xaxis and yaxis labeled correctly with units. 
Axes contain minor flaws. Graph is titled. 
Axes contain minor flaws or no title to graph. 
Axes contain major flaws with no title on graph. 

Analyze graphs 
Line of best fit is neatly drawn properly and slope of line is correct. All work is shown. 
Line of best fit is drawn properly and slope of line is correct but with minor errors. 
Line of best fit is drawn with slight error. Slope of line not accurate. 
Line of best fit is missing. Major error in slope of line. 

Determine Relative error 
Percent of error correct and within acceptable range. 
Percent of error has minor flaws but is within acceptable range. 
Percent of error has minor flaws and is not within acceptable range. 
Percent of error is not shown or is too large. 

Verify relationships found through analysis of graphs 
Mathematical relationships are clearly and accurately verified. 
Mathematical relationships are accurately verified. 
Mathematical relationships are not accurately verified. 
Mathematical relationships are not verified. 

Answer discussion questions 
Answers to discussion questions are complete and logical. 
Answers to discussion questions are not complete or contain flaws. 
Answers to discussion questions are not complete AND contain flaws. 
Answer to discussion questions missing or contain major flaws. 
Resources:
http://www.teachersdomain.org/asset/lsps07_int_circmotion/
http://www.polyhedronlearning.com/hsvpl/centripetalforce/cfframeset.html
http://www.polyhedronlearning.com/index.html
http://www.youtube.com/watch?v=TahcJy1AlXI&feature=player_embedded
Teacher Notes:
Lab may also be done using a Centripetal Force Apparatus Kit and
Centripetal Force Lab Handout .
Misconceptions:
Some students believe objects experience an outward force when travelling in circular motion. Students may view the following to help them with this misconception
Video:
Misconceptions: Centripetal vs. Centrifugal
By sciencefaction
http://youtu.be/weeiZjzQo
Prezi
Centrifugal Force  The Misconceptions
by Jay Douglas
http://prezi.com/rvwxxl3nkrep/?utm_campaign=share&utm_medium=copy
Other ways to engage students on circular motion.
Video:Car on a Level Track, Michael Gallis http://youtu.be/TahcJy1AlXI
Video: Real World  Centripetal Force
NASAeClips http://youtu.be/PBpe_LLlQJw
Other discussion questions can be found at the following link.
Discussion questions