GEN PHYS 1 | Unit Vectors and Work, Energy, & Power

Component Form of Vectors

it simplifies operations by breaking down vectors into their individual components

Unit Vector

• It has a magnitude of 1 and no units as it only aims to point to a direction in space.

• It has a caret (^) to distinguish it from ordinary vectors.

• common for three dimensions as it requires z-axis

Unit Vector Formula (does not include caret)

A = A_xi + A_yj + A_zk

Dot Product

Known as the scalar product, it is equal to A • B. The quantity will end up being scalar.

Definition of Dot Product (w/ angle)

|A|•|B|cos(angle between both vectors)

Component Formula

A • B = A_xB_x + A_yB_y + A_zB_z

Angles and Dot Product

• If the angle is zero, then the formula is |A|•|B|

• If the angle is 90º, then the dot product is zero.

• Otherwise, assume the formula as normal

Vector Product

• measures how parallel the vectors are

• also known as the cross product

• the product is a vector

• C = ABsinΘ

Work

measure of energy transfer that occurs when an object is moved over a distance by an external force

Unit of Work

Joule (J) or N•m

Positive Work

force and displacement have components that move in the same direction

Negative Work

force and displacement have components that move in the opposite direction

Zero Work

Occurs when:

1. Force = 0

2. Displacement = 0

3. Force and displacement are perpendicular or form a 90º angle.

Work with Variable Force

If the force changes with position, work is the area under the Force vs Position graph.

Energy

the ability to do work; property that must be transferred to an object to do work

Mechanical Energy

includes potential and kinetic energy

Potential Energy

energy that is formed due to the object’s position, orientation, or composition

Kinetic Energy

energy that is formed due to the object’s motion

Conservative Force

• work done is path-independent and can be expressed via a potential energy function

• examples include gravity and spring force

Non-conservative Force

• work depends on the path and dissipates energy as heat

• examples include friction and air resistance

Power

the rate which work is done or energy is transferred over time

Unit of Power

Watts or joules/second