Work, Power, Energy, Momentum, Impulse, Collisions

• Understanding work, power, energy, momentum, impulse, and collisions is essential for describing object interactions and energy transfer in physics.

Work, Power, and Energy

• Work is the energy transfer to or from an object via force application along a displacement.
• Work equals ( W = F \cdot d \cdot \cos(\theta) ), where ( W ) is work, ( F ) is force magnitude, ( d ) is displacement, and ( \theta ) is the angle between force and displacement vectors.
• Power measures the rate at which work is done or energy is transferred.
• Power equals ( P = \frac{W}{t} ), where ( P ) is power, ( W ) is work, and ( t ) is time.
• The SI unit for power is the watt (W), equivalent to one joule per second.
• Energy is the capacity to do work and exists in various forms.
• Kinetic energy is the energy possessed by an object due to its motion.
• Kinetic energy equals ( KE = \frac{1}{2} m v^2 ), where ( m ) is mass and ( v ) is velocity.
• Potential energy is stored energy based on position or configuration.
• Gravitational potential energy equals ( PE = m g h ), where ( g ) is the acceleration due to gravity and ( h ) is height.
• In a closed system with only conservative forces, total mechanical energy (kinetic and potential energy) remains constant.
• Conservation of mechanical energy is expressed as ( KE_{\text{initial}} + PE_{\text{initial}} = KE_{\text{final}} + PE_{\text{final}} ).

Collision, Impulse, and Momentum

• Linear momentum is a vector quantity defined as the product of an object's mass and velocity.
• Momentum equals ( p = m \times v ), where ( m ) is mass and ( v ) is velocity.
• Momentum indicates the amount of motion and an object's resistance to changing that motion.
• Impulse measures the change in momentum resulting from a force applied over a time interval.
• Impulse equals ( J = F \times \Delta t ), where ( F ) is force and ( \Delta t ) is the time interval.
• Impulse equals the change in momentum (( \Delta p )), shown as ( J = \Delta p ).
• Elastic collisions conserve both momentum and kinetic energy, and objects rebound without lasting deformation or heat generation.
• Inelastic collisions conserve momentum, but kinetic energy is not conserved, and some kinetic energy transforms into other energy forms.
• Completely inelastic collisions are when objects stick together after impact, moving as one entity.
• In an isolated system with no external forces, total linear momentum before and after a collision remains constant.
• Conservation of linear momentum is expressed as ( \sum p_{\text{initial}} = \sum p_{\text{final}} ).