Physics: Energy and Work

Work is the component of force in the direction of motion times the distance moved.
W = Fd, where W is work, F is force, and d is distance.
Units of work are Newton-meters (N*m), also known as Joules (J).

Kinetic energy is the energy of motion.
Kinetic energy = ½ mv^2, where m is mass and v is velocity.
The kinetic energy of a moving object is equal to the work required to bring it from rest to that speed, or the work the object can do while being brought to rest.

Energy cannot be created or destroyed, only transformed from one form to another.
The total amount of energy remains constant.

A machine is a device that increases or decreases a force or changes the direction of a force.
Examples of machines include levers and pulleys.
The work output of a machine cannot exceed the work input.

Efficiency is the percentage of the work put into a machine that is converted into useful work output.
Efficiency = (useful energy output) / (total energy output) * 100.

Momentum is directly proportional to velocity, while kinetic energy is proportional to v^2.
Momentum and kinetic energy are related but distinct concepts.

Example Problem 1: Calculate the work required to lift a 300-kg refrigerator to a second-floor level.
Example Problem 2: Compare the change in kinetic energy resulting from exerting different forces over different distances.
Example Problem 3: Calculate the weight of a load lifted using a lever.
Example Problem 4: Calculate the maximum force exerted by a hydraulic machine.
Example Problem 5: Analyze the energy transformation in an inelastic collision between two freight cars.
Example Problem 6: Calculate the fuel efficiency of a car engine.
Example Problem 7: Calculate the change in gravitational force between two planets when the distance between them is decreased.
Example Problem 8: Calculate the velocity of a ball thrown horizontally from a cliff.
Example Problem 9: Calculate the velocity of a cannonball at the top of its trajectory.
Example Problem 10: Calculate the horizontal velocity required for a person to jump from a high-rise balcony to a swimming pool.
Example Problem 11: Calculate the hang time for a person during a high jump.

Law of Universal Gravitation: everything pulls on everything else with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
F = (Gm1m2) / (d^2), where G is the gravitational constant.

F = (Gm1m2) / (d^2), illustrating the inverse-square relationship between force and distance.

Weight is the support force experienced by an object, which can be affected by external accelerations.
Astronauts in orbit are in a state of apparent weightlessness due to the absence of a support force.

During projectile flight, velocities in both the vertical and horizontal directions can be considered.
Projectiles launched horizontally maintain their horizontal velocity, while those launched at an angle have different proportions of velocity in the horizontal and vertical directions.
Air drag affects the trajectory of projectiles, and optimal launching angles vary depending on the specific situation.
Satellites are projectiles that fall around the Earth rather than into it, and are in a state of continuous free fall.