Understanding Kinetic and Potential Energy Concepts

Kinetic energy at Position A vs B

Less (At a higher position, the marble has more potential energy and less kinetic energy. As it moves down, KE increases.)

Work done when pushing an object twice as far

Twice as much work (Work = Force × Distance, so doubling the distance doubles the work.)

Mechanical energy

The sum of kinetic energy and all forms of potential energy (Mechanical energy = KE + PE, which includes gravitational and elastic potential energy.)

Mechanical energy in the presence of friction

It is no longer conserved (Friction converts mechanical energy into heat and sound, which are nonmechanical energy forms.)

Kinetic energy of a 29.4 N toy falling from 1.00 m

29.4 J (All potential energy is converted into kinetic energy: PE = mgh = 29.4 J.)

Work done when pushing an object with twice the force and distance

Four times as much (Doubling force and distance results in 2 × 2 = 4 times the work.)

Main types of simple machines

Levers, inclined planes, pulleys (There are six types: levers, inclined planes, pulleys, wheel & axle, screws, and wedges.)

Output energy of a simple machine

No (Simple machines reduce effort by redistributing forces, but they do not create energy.)

Kinetic energy gain of a falling object

Yes (As it falls, gravitational potential energy is converted into kinetic energy.)

Potential energy of a moving object

Yes (An object can be moving and still have stored potential energy, like a pendulum at its highest point.)

Gravitational potential energy

The energy an object has because of its height above the ground.

Factors affecting gravitational potential energy

Mass and height (since PE = mgh).

Kinetic energy

The energy of motion, calculated as KE = ½mv².

Law of conservation of mechanical energy

In a frictionless system, total mechanical energy (PE + KE) remains constant.

Potential energy when an object falls

It converts into kinetic energy.

Kinetic energy when an object moves upward

It converts into potential energy.

Frictionless surface

No energy is lost to friction, so mechanical energy is conserved.

Finding new height using conservation of energy

Use conservation of energy: PE_i = PE_f + KE_f and solve for h_f.

Mass cancellation in conservation of energy

Because mass is in every term, it divides out of the equation.

Unit for energy

Joules (J).

Difference between weight and mass

Mass is the amount of matter (kg), while weight is the force due to gravity (N).

Rearranging conservation of energy equation for height

h_f = h_i - (KE / mg).