physics week 10 part 1

If an object is in motion, it possesses kinetic energy.
- Kinetic Energy Formula:
- The formula to calculate kinetic energy is given by: KE = rac{1}{2} m v^2
  - Where:
    - KE represents kinetic energy.
    - m is the object's mass.
    - v is the object's speed (not velocity).
Important Note about Energy:
- Energy is a scalar quantity, meaning it only has magnitude and no direction. This differentiates energy from vector quantities.
- In this context, it is unnecessary to utilize velocity; only the speed of the object matters.
Common mistake:
- Students often relate energy with the components of velocity, such as thinking about energy in terms of the x or y components. This is incorrect because energy does not depend on direction.

The relationship between an object's kinetic energy and work done on it:
- Work done on an object is directly equivalent to the change in its kinetic energy.
- Essentially, if a net force causes work on an object, it will result in a change in kinetic energy.
- Intuitive Concept:
  - When a net force is applied to an object, it accelerates, leading to a change in speed (and therefore kinetic energy).
When a force applies negative work (e.g., in the opposite direction), it causes a decrease in kinetic energy.
- Example: Overcoming static friction before acceleration is necessary, demonstrating that friction can prevent initial acceleration.

At this initial stage, friction is not taken into account in calculations; it will be addressed in subsequent lessons.

Two primary forms of energy:
- Kinetic Energy: Energy of motion.
- Potential Energy: Energy of position or configuration.
Conservative Forces:
- Defined as forces for which work done is path-independent (it only depends on initial and final positions).
- Examples include gravitational forces and spring forces.
Potential Energy of a Spring:
- Formula:
- PE = rac{1}{2} k x^2 where:
  - PE is the potential energy,
  - k is the force constant of the spring,
  - x is the displacement from the equilibrium position.
The work done on a spring, irrespective of the chosen path, solely depends on the initial and final lengths relative to the rest position.

When moving an object vertically in a gravitational field:
- The work done against gravity can be expressed as:
- W = -mg imes h where:
  - W is work done,
  - m is mass,
  - g is acceleration due to gravity,
  - h is the height displacement.
Reference Points for Potential Energy:
- For gravitational potential energy, the ground is often chosen as the zero potential energy reference point.
- Potential energy can be negative if moving below the reference point.

When an object falls, its potential energy decreases while its kinetic energy increases.
As long as only conservative forces are acting, the conserved total mechanical energy can be described as:
- E_{total} = KE + PE
Example scenario: Child sliding down a ramp:
- At the bottom of the ramp, potential energy equals zero, thus:
- All energy has transformed into kinetic energy, represented as:
  KE = rac{1}{2} m v^2
It is emphasized that the x and y components of motion are irrelevant when utilizing energy methods compared to kinematic approaches.

Problem-solving strategy includes:
- Drawing a Diagram: Visual representation aids in understanding the scenario.
- Identifying Events: Establish characteristics at different points (e.g., top and bottom of a ramp) to analyze energy changes systematically.
Example:
- Initial event at top of the ramp marked as Event 0, with considerations for mass and speed as per problem prompts.