Work And Energy Basic Concepts Related To Constant And Variable Forces Kinetic Energy

Concepts on Work done by Constant Force:

• Work Done By Variable Forces: is the sum of the work done by the constant force and the variable force.

• Scalar Product: is a mathematical operation that takes two vectors as inputs and produces a single number as output. It is also known as the dot product.

• Dot Product: is defined as the product of the magnitudes of the two vectors and the cosine of the angle between them.

• Dot Product in Components Form: $$ \vec{A} \cdot \vec{B} = A_x B_x + A_y B_y + A_z B_z $$

• Work Done with variable Force acting at an Angle: If the force acting on an object is variable in magnitude and/or direction, the work done can be calculated using the following equation: $$W = \int_s \vec{F} \cdot d\vec{r}$$

Kinetic Energy:

• Work-Energy theorem: It states that the net work done on an object is equal to its change in kinetic energy. That is: $$W_{net} = \Delta K$$