Work

• Definition: A force of magnitude F acting on an object that moves by a distance d, at an angle with respect to the displacement of the object, does a work W = Fd cos on it.
• Sign: If W > 0 (W < 0) then the force tends to accelerate (decelerate) the object's motion.

Kinetic Energy

• Definition: The energy an object has because of its motion, KE = (1/2) mv².
• Relationship with work: The net work done by all forces on an object between two points equals the change in KE of the object between those two points, KE = W_net.

Potential Energy

• Definition: The energy an object has because of its location with respect to sources of force. A force can be used to define a potential energy if it is conservative: the work it does between two points doesn't depend on the path taken between those two points.
• For gravity near Earth's surface: The potential energy is PE_G = mgy, where y is the height from any reference point chosen for a given problem.
• Elastic force: The force is given by Hooke's law, F_S = –kx, where k is the spring's stiffness constant, and the potential energy is PE_S = (1/2) kx².

Conservation of Energy

• Most general statement: The total amount of energy in the universe remains constant.
• Individual object: Its energy is the sum E = KE + PE + E_internal, and it can change when it interacts with other objects and its environment, for example because of work done on the object (or heat added to it).
• Mechanical energy: The sum E_mech = KE + PE. If all the forces that do work on an object are conservative, then the object's mechanical energy remains the same. This can be written as KE + PE = constant, or KE + PE = 0, or E₁ = E₂. Otherwise, if some forces are non-conservative and/or heat is added, KE + PE = W_other + Q, or E₁ + W_other + Q = E₂.

Power

• Definition: The average power produced/used/transmitted over a time t is P = E/t.