Honors Physics - Chapter 5: Lesson 2

Chapter 5: Lesson 2

Vectors

Chapter 5: Lesson 2 - Vectors

Review of Vectors:

Remember, vectors have both magnitude and direction. The resultant vector is the result of adding two or more vectors together. If the vectors are pointing in the same direction, you can add them. If the vectors are pointing in the opposite direction, you have to subtract them.

Vector Components

Any single vector (like the blue one in the picture) can be thought of as a resultant of two vectors, called components.

Usually the components are chosen to be perpendicular to each other. Look at the picture. There is a vertical component and a horizontal component that form a right triangle.

The process of finding the components of a single vector is called vector resolution.

A vector which is directed northwest can be thought of as having two parts - a northward and a westward part.

A vector which is directed upward and rightward can be thought of as having two parts - an upward and a rightward part.

Look at the three pictures above. When the dog's leash is vertical, there is no horizontal component. When the dog's leash is horizontal, there is no vertical component. When the dog's leash is at some angle to the horizontal, there is both a horizontal and a vertical component.

Using trigonometry, we can figure out the horizontal and the vertical forces that are acting on the dog if the tension on his leash is 60 N.

Check Your Understanding:

Click on the down arrow when you have your answer to check to see if you are correct.

The arrow to the left depicts a force which makes an angle to the horizontal. This force will have horizontal and vertical components. Which one of the choices below best depicts the direction of the horizontal and vertical components of this force?

Choice d. The arrow to the left is going both down and to the left, so you need two components, one that is going down and one that is going to the left.

Equilibrium

The figure here shows the addition of three forces, A, B, and C. The three vectors form a closed triangle.

When three or more vectors form a closed shape when added together, there is no net force. All the vertical components cancel out and all the horizontal components cancel out. A is pointing up, but the vertical component of B is pointing down. That cancels out. C is pointing to the left, but the horizontal component to B is pointing to the right. That cancels out.

When the vectors form a closed shape, the net force is zero, so the object is in equilibrium.

Equilibrant

The equilibrant is equal and opposite to the resultant. In the picture, vectors A and B are added together to form the resultant R. The equilibrant is equal and opposite to the resultant R. It is the force that equals out the resultant.

Be very careful not to mix up the words equilibrium and equilibrant.

It is easy to do and they mean very different things!

Lets apply what we know about vectors and trig to Physics

A hiker leaves camp and hikes 11 km, north and then hikes 11 km east. Determine the resulting displacement of the hiker.

To do this, you would just use the pythagorean theorem since the two distances are perpendicular to each other. Look at the picture to see the work.

The Motor Boat Problem

A well known physics problem dealing with vectors is the motor boat problem. Look at the questions below and then click on the video to hear my explanation.

A motor boat traveling 4 m/s, East encounters a current traveling 3.0 m/s, North.

A. What is the resultant velocity of the motor boat?

B. If the width of the river is 80 meters wide, then how much time does it take the boat to travel shore to shore?

C. What distance downstream does the boat reach the opposite shore?

You have finished Lesson 2!

Be sure to head over to google classroom and fill out the exit pass.

Report abuse