# Understanding Vectors - Vector Addition

#### Summary

By participating in a group activity, students will learn how to add force vectors. They will see the significance of direction when adding vector quantities.

## Learning Goals

Following this activity, students will be able to:

- Differentiate between scalar and vector quantities.

- Graphically add vectors.

- Identify examples of vectors and scalars.

- Differentiate between scalar and vector quantities.

- Graphically add vectors.

- Identify examples of vectors and scalars.

## Context for Use

This activity is designed for physics classes and can be completed in one 50 minute period. Its purpose is to clearly impress upon students the difference between vector and scalar quantities, and the importance of considering direction when dealing with vectors. It is appropriate as an introduction to vectors and vector addition.

**Subject**: Physics:General Physics:Vector Algebra

**Resource Type**: Activities:Classroom Activity:Short Activity:Demonstration, Activities:Classroom Activity

**Grade Level**: High School (9-12)

## Description and Teaching Materials

This activity follows a brief introduction to vectors and scalars. Both types of quantities are defined and examples of each are identified.

The actual activity begins by hanging a two kilogram mass from a spring scale which is calibrated in Newtons. The reading will be approximately 20 N. Then the same mass is suspended from a string (approximately 2 meters long) which is hanging from two spring scales which are attached to the blackboard. The mass is not placed in the middle, but closer to one end than the other. The readings of both spring scales are recorded, and the direction of force of each spring scale is marked by tracing the string on each side of the mass. An appropriate scale is chosen, and vectors are drawn to represent the force of each spring scale. When the force vectors are added to each other, the resultant should be very close to 20 N straight up (to balance the weight of approximately 20 N down). It becomes clear that adding the magnitudes of the two forces as scalars gives an incorrect total force, but adding them as vectors gives an appropriate resultant force.

-One 2 m piece of string

-One 2 kg mass

The actual activity begins by hanging a two kilogram mass from a spring scale which is calibrated in Newtons. The reading will be approximately 20 N. Then the same mass is suspended from a string (approximately 2 meters long) which is hanging from two spring scales which are attached to the blackboard. The mass is not placed in the middle, but closer to one end than the other. The readings of both spring scales are recorded, and the direction of force of each spring scale is marked by tracing the string on each side of the mass. An appropriate scale is chosen, and vectors are drawn to represent the force of each spring scale. When the force vectors are added to each other, the resultant should be very close to 20 N straight up (to balance the weight of approximately 20 N down). It becomes clear that adding the magnitudes of the two forces as scalars gives an incorrect total force, but adding them as vectors gives an appropriate resultant force.

**Materials needed:**

-2 spring scales calibrated in Newtons-One 2 m piece of string

-One 2 kg mass

## Teaching Notes and Tips

By placing the suspended mass off center, vectors of different magnitudes are obtained.

Spend adequate time dealing with how to measure angles when adding the vectors.

Spend adequate time dealing with how to measure angles when adding the vectors.

## Assessment

Guided and independent practice in vector addition will follow this activity. The unit exam will include vector addition problems.

## Standards

II.D.1 Motion

II.E.1,2 Forces of Nature

II.E.1,2 Forces of Nature