Physics1

Definition of Energy and Work

• Energy: The ability to do work.

• Work: Defined mathematically as W = F · d, where F is the force applied, d is the displacement, and the dot indicates a special multiplication involving the angle between the two vectors.

  • Work is dependent on the component of force in the direction of the displacement.

  • If the angle between force and displacement is 90 degrees (perpendicular), work done is zero.

Illustrative Examples

• Pushing a Lawn Mower: When pushing at an angle, only the horizontal component of the force contributes to moving the mower forward, while the vertical component increases normal force and friction.

  • Better to Pull than Push: Pulling reduces the normal force, thus reducing friction compared to pushing an object.

Work-Energy Theorem

• The theorem states that net work done on an object is equal to the change in its kinetic energy (ΔKE = W_net).

• Kinetic Energy (KE): Given by the formula KE = 1/2 m v², where m is mass and v is velocity.

  • An object at rest has zero kinetic energy, and doing work on it gives it kinetic energy.

Forces and Motion

• To lift an object at a constant speed, the upward force equals the downward gravitational force (mg). The work done is W = F · d = mgh when elevating an object against gravity.

  • Gravity's negative work: While doing positive work to lift, gravity does negative work equal to -mgh.

• The concept of net work becomes significant when throwing an object upwards or moving it horizontally at constant speed, as forces affect the net work done.

Conservation of Energy

• Law of Conservation of Energy: Total energy remains constant in a closed system; energy can transform but not be created or destroyed.

  • Energy transformations occur from potential energy (PE) to kinetic energy (KE) and vice versa, especially in gravitational fields.

Key Physics Principles

• Work is both how you add energy to a system (e.g., moving an object) and how you remove energy (e.g., friction slowing an object).

• A scalar product yields a scalar quantity, signifying that while work has a magnitude, it does not possess direction like vectors.

• The efficiency of work done to achieve motion is highly dependent on angles of application of force and motion.