# Centripetal Force Activity

## Classroom Set

### Materials Included In Kit

Handle tubes, 8
Paper clips, 16
Rubber stoppers, two-hole, 8
String, 14 meters
Washers, 160

Graph paper
Meter stick
Stopwatch or clock with second hand
Balance, 0.1-g precision

### Prelab Preparation

Cut the 14 meter string into 1.5 m lengths. Each group of students will need one 1.5-m piece.

### Safety Precautions

This lab is best conducted outdoors, in an open gymnasium or other large open area. All students should wear safety glasses whenever anyone is conducting the experiment in the area. You might check each experimental setup before the twirling begins. Have students spread out as much as possible. Please follow all laboratory safety guidelines.

### Disposal

All materials in the kit may be reused many times.

### Teacher Tips

• Be very alert about safety during this lab. If students spin the apparatus too violently, projectiles can fly around unexpectedly. Try to find an open area where students can spread out and thus decrease the chance of flying objects hitting anyone or anything. Be sure that students spin the rubber stoppers and not the paper clips or washers!
• The amount of theory to cover relative to centripetal force will be dictated by your students and course goals. Most physics texts describe a derivation of the formula provided in the student background. The derivation involves vector solutions. Use your judgment about how much of the derivation should be discussed. Please consult a physics textbook for a more thorough explanation.

### Science & Engineering Practices

Developing and using models
Planning and carrying out investigations
Analyzing and interpreting data
Using mathematics and computational thinking
Constructing explanations and designing solutions
Engaging in argument from evidence

### Disciplinary Core Ideas

HS-PS2.A: Forces and Motion

### Crosscutting Concepts

Patterns
Cause and effect
Scale, proportion, and quantity
Systems and system models

### Performance Expectations

MS-LS1-2: Develop and use a model to describe the function of a cell as a whole and ways parts of cells contribute to the function.

### Sample Data

Part II. Measuring the Force {12731_Data_Table_1}

# Centripetal Force Activity

### Introduction

Have you ever been on a human centrifuge at an amusement park? You can certainly feel the tremendous force being imposed upon your body as you travel in a circular fashion—so much force that when the floor drops away, you are pinned against the wall!

### Concepts

• Centripetal force
• Centripetal acceleration
• Velocity
• Newton’s laws of motion

### Background

Centripetal force is the “center seeking” force that makes an object move in a circle. According to Newton’s first law, when an object is in motion, it will remain in motion unless acted upon by an unbalanced force. This means an object will travel in a straight line at a constant speed as long as no outside force is acting on it. In order for an object to move in a circle, an inward force is needed. For example, imagine a rubber stopper being whirled around on the end of a string. The hand holding the string exerts an inward force (centripetal) on the rubber stopper (see Figure 1). If the string were to break, the stopper would fly outward in a straight line. The mathematical expression for centripetal force is the same as for any other force, based on Newton’s second law of motion: {12731_Background_Figure_1} {12731_Background_Equation_1} F is the force (N) m is the mass (kg) a is the acceleration (m/s2) According to Equation 1, a force will cause an object to accelerate. Therefore a centripetal force will pull an object toward the center of the circle causing a centripetal acceleration. The formula for centripetal acceleration can be derived from vector analysis of the forces on a circle: {12731_Background_Equation_2} a is the centripetal acceleration v is the velocity of the object (tangent velocity) r is the radius of the circular path of the object According to Equation 2 and Figure 1, an object whirled around should accelerate toward the center of the circle, because the centripetal force is pulling it inward. But why does it not get pulled right into the center of the circle? The reason for this is due to the tangent velocity of the object. The tangent velocity of the object actually prevents it from being pulled into the center. For more information on the relationship between tangent velocity and centripetal acceleration, consult a physics textbook. Now if we substitute Equation 2 into Equation 1, centripetal force can be expressed as Equation 3. {12731_Background_Equation_3} Notice that in order to solve for the centripetal force using Equation 3, the mass and velocity of an object, as well as the radius of its circular path, must be known. The mass can easily be measured using a balance, and the radius can be measured with a meter stick. But how can the velocity of the object be measured? The typical equation for calculating the average speed (v) of an object can be used to determine the velocity. {12731_Background_Equation_4} Now the question is, how can you find the distance around a circle? When an object makes one complete revolution, it travels a distance equal to the circumference of a circle, 2πr. The time it takes for one complete revolution around a circle is known as the period, T. Therefore, for objects moving in a circle, the velocity can be expressed as Equation 5. {12731_Background_Equation_5} v is the velocity (m/s) r is the radius of the circular path (m) T is the period – time for one revolution (s)

### Experiment Overview

The purpose of this lab activity is to determine the relationship between the velocity and centripetal force of an object moving in a circle.

### Materials

Balance, 0.1-g precision
Graph paper
Handle tube
Meter stick
Paper clips, 2
Rubber stopper, two-hole
Stopwatch or clock with second hand
String, 1.5 m
Washers, 20

### Safety Precautions

The very nature of the motion in this activity makes it potentially dangerous. Use caution when twirling the rubber stopper. This lab is best conducted outdoors, in an open gymnasium, or other large open area. Wear safety glasses whenever your group or anyone else is conducting the experiment in the area. Please follow all laboratory safety guidelines.