Module 5—Circular Motion

Lesson 1 Lab: Inward Force and Circular Motion

 

Introduction

 

When an object travels in a circular path, there must be an inward force causing the direction of the motion to change. This is a direct application of Newton's first and second laws of motion. There is a relationship between the size of the force and the speed of the object, the mass of the object, and the radius of the arc through which the object moves. You can feel the force by whirling an object at the end of a string. This lab activity will be used to investigate and produce a precise mathematical expression that describes these relationships.

 

What is the precise mathematical relationship between inward force and the variables velocity (v), mass (m), and radius (r) for an object rotating in a horizontal plane?

 

Prediction

 

The relationship between the inward force and each variable will show one of three graphical relationships. These reference graphs illustrate the respective mathematical relationships between the variables x and y.

 

Graphical Analysis Reference Tables
y varies directly as x	y varies as the inverse of x	y varies as x squared

 

Problem 1

 

How is inward force related to speed?

 

Procedure

 

Re-open the Circular Motion: Horizontal simulation, if necessary, and continue with the procedure.

• Set the mass to 1.0 kg and the radius to 1.0 m.

• Run the simulation, and adjust the initial velocity to the values shown in the table below.

Observations and Analysis

 

Self-Check

 

SC 5. Record the inward force (tension) for each speed in the table below.

 

Speed (m/s)	Inward Force (tension) (N)
1.0
2.0
4.0
8.0
10.0
12.0
15.0
20.0
25.0

 

SC 6. Use the data from SC 5, and sketch the graph in the space provided below. (Note: You may enter this data into a spreadsheet and use the spreadsheet’s graphing capabilities.)

 

 

 

SC 7. Compare your graph to the table from SC 5, and state the relationship between the inward force and the speed. Substitute the term Fc for y and the term v for x.

 

 

(Note: We cannot use the vector sign for the force because the force and speed are not in the same directions. Thus, only the magnitudes are indicated.)