🟢 CONSERVATION OF ENERGY BASICS

Law of Conservation of Energy

Energy cannot be created or destroyed; it can only be transformed from one form to another.

Mechanical Energy (ME)

The total of kinetic energy (KE) and potential energy (PE). Formula: ME = KE + PE.

Kinetic Energy (KE)

Calculated using the formula KE = ½ × m × v², where m is mass and v is velocity.

Gravitational Potential Energy (PE)

Calculated using the formula PE = m × g × h, where m is mass, g is acceleration due to gravity (9.8 m/s²), and h is height.

Elastic Potential Energy (PE_spring)

Calculated using the formula PE_spring = ½ × k × x², where k is the spring constant and x is compression/stretch.

Spring Constant (k)

A measure of how stiff a spring is; higher k means a stiffer spring. Units are N/m.

Work

Calculated as Work = Force × Distance × cos(θ); it is a way of transferring energy.

Energy Transfer (KE = PE)

Occurs when energy is transferred between motion and height, assuming no energy losses (like friction).

No Energy Losses

Indicates that friction and air resistance can be ignored, so total energy remains constant.

Energy Loss to Heat or Friction

Calculated as Energy lost = Initial energy - Final mechanical energy.

Relationship Between Energy and Speed

More KE indicates higher speed; losing KE results in lower speed. KE = ½mv² leads to v = √(2KE/m).

Ramp and Spring Formula

When an object moves up a ramp and compresses a spring: Initial KE + Initial PE = PE_spring; ½mv² + mgh = ½kx².

Falling onto a Spring Formula

Start with potential energy: PE = mgh; at max compression: PE_spring = ½kx²; mgh = ½kx².

Speed Before Impact Formula

Use PE = KE to find speed: mgh = ½mv²; solve for v: v = √(2gh).

Force of Friction

Work by friction equals change in energy; F = Energy lost / distance.

Handling 10% Energy Loss Questions

Total energy × 90% gives energy still available for KE or PE calculations.

Value of Gravity (g)

9.8 m/s².

At Rest (for KE)

If an object is at rest, its velocity is 0, resulting in KE = 0.

Minimum Work

Calculated as Work = change in energy, usually PE; W = m × g × Δh.

Compressed Spring Definition

If something is compressed by a spring, it stores elastic potential energy given by PE_spring = ½kx².