Physics - Energy and Momentum - High School and AP Physics

Explore energy as the ability to do work, define potential, kinetic, and elastic energies, and learn how work changes energy and drives conservation of energy.

Explore how work changes energy through force times distance parallel to motion, including positive, negative, and zero work, net work, friction, and conservation of energy.

Understand gravitational potential energy, its formula P = m g h, and how lifting a mass adds energy through work, using height as a reference point.

Present kinetic energy as the energy of motion and the work required to stop, using KE = 1/2 m v^2 for a 100 kg box at 4 m/s and friction.

Explore springs within energy and momentum, applying Hooke's law F = -kx, understanding displacement from equilibrium, and calculating elastic potential energy 1/2 k x^2 in real-world systems.

Explore power as the rate at which work is done, its units in watts, and its relationship to force, distance, and average velocity, with stairs and horsepower examples.

Learn how the conservation of energy keeps mechanical energy constant: the sum of potential and kinetic energy, minus friction losses, with roller coaster examples illustrating energy transfer.

Explore conservation of energy in a spring-mass system by converting elastic potential energy to kinetic energy to determine speed, then to gravitational potential energy to determine height, neglecting friction.

Analyze a rough-surface energy problem, derive that friction equals the applied force to maintain velocity, then use work-energy to find a 35-newton force and 1.5 m/s^2 acceleration.

Minimum work to compress the spring is 150 joules, converting to the kinetic energy of the three-kilogram mass moving at 10 m/s on a frictionless table.

Use energy conservation on a swinging pendulum-like system to derive the speed at the lowest point in terms of g, r, and theta, then examine tension via circular motion.

Explore a 1986 AP energy problem that combines spring potential energy, kinetic energy, and projectile motion on a frictionless table, deriving time of flight, horizontal velocity, and the spring constant.

Use energy conservation to solve a swinging monkey problem, equating potential energy to kinetic energy at the lowest point, then compute the tension in vine B.

Explore momentum as mass times velocity, a vector that makes moving objects hard to stop, with its unit kilogram meter per second and the p notation.

Explore how momentum changes under Newton's second law by linking net force to the rate of momentum change, via changes in mass and velocity and related examples.

Explore how impulse equals the change in momentum, defined as force times time, and how net force is the rate of momentum change, while increasing contact time reduces impact force.

Explore conservation of momentum in a closed system, where total momentum before equals after, and distinguish elastic collisions that conserve momentum and kinetic energy from inelastic ones that lose energy.

Explore momentum conservation through solved examples of elastic and inelastic collisions, calculating before-and-after momenta and final velocities, and examining recoil.

Learn conservation of momentum in two dimensions by treating x and y separately, applying before equals after for each axis, with a two-body collision illustrating velocity components and angles.

Use momentum conservation to analyze a bullet-block collision on a frictionless surface; the block ends at v0/6, and the bullet loses 4/9 m v0^2 of energy.

Solve a momentum problem involving a block and a toboggan using projectile motion and momentum conservation. The final speed when they move together is v = (M1 v0)/(M1+M2).

an inelastic collision on a frictionless surface between mass M and a 2m block attached to a spring, derive velocity via momentum conservation and relate kinetic energy to spring compression.

Two objects, 1 kg and 4 kg, collide with speeds 60 m/s and 5 m/s at 37 degrees; compare momentum components before and after, and show energy is not conserved.