Energy 1. Work 2. Kinetic Energy 3. Work-Energy Principle 4. Friction 5. Potential Energy 6. Conservation of Energy ©2013 Robert Chuckrow

1. Work Work W is defined as the part of the force in the direction of the motion multiplied by the distance moved: W = F // x d. Note: The part of the force perpendicular to the motion does no work. Question: Can work ever be negative?

Answer to Q. 1, and a new Question Answer: Yes, work done by a force is negative if the direction of the force doing the work is opposite to that of the motion (slowing the object down). Question 2: Can a force exerted on a moving object ever do zero work?

Answer to Q. 2, and a new Question Answer: Yes, a force exerted on a moving object can do zero work if it is perpendicular to the motion. Question 3: Are there other cases in which a force exerted on an object does zero work?

Answer to Question 3 Answer: Yes, a force exerted on a stationary object does zero work. Summary: (a) The work done by a force is negative when the direction of the force is opposite to that of the motion. (b) A force does zero work if it is perpendicular to the motion. (c) A force does zero work if it is exerted on a stationary object.

2. Kinetic Energy The Kinetic Energy (KE) of a mass m, moving with speed v is defined: KE  mv  . Question: By what factor does the KE of an object change if: (a) its mass is doubled, but its velocity remains the same? (b) its velocity is doubled, but its mass remains the same?

Answer Recall, KE  mv  . (a) If an object’s mass is doubled, keeping its velocity the same, its KE doubles. (b) If an object’s velocity is doubled, keeping its mass the same, its KE quadruples.

3. Work-Energy Principle The Work-Energy Principle: The work done by all forces on an object equals its change in kinetic energy. Work total = Change in KE Think: Check the consistency of the above principle with Newton’s first and second laws.

4. Friction When an object moves on a “rough” surface, the direction of the force of friction is always opposite to that of the motion. Consequently, friction does negative work. When friction causes a moving object to slow down, the negative work done by friction reduces that object’s KE. It might seem that the energy of the moving object is thereby totally lost, but actually, it becomes microscopic KE; namely, the random jiggling of molecules of the object and surface increases. That is, their thermal energy increases (their temperature rises). Because it is random, thermal energy is very hard to retrieve, so as far as mechanical energy is concerned, it is lost.

5. Potential Energy Lift a mass m through a height h. The work I do will be mg x h. Where did the energy go? Answer: It is potentially available because, if I drop the mass, gravity will do mg x h of work on the mass—the same amount of work that it took to lift it. Therefore, by my lifting the mass, the energy I expended was not lost but went into potential energy = mgh. Note: The word potential comes from the word potent (having power), so potential means having power that has not yet been brought into being.

6. Conservation of Energy We also say that during its way down, the falling mass lost potential energy (PE), which was converted into kinetic energy (KE). Thus, in this case, where gravity is the only force doing work, mechanical energy (PE + KE) is conserved (not lost). Example: When you throw a ball vertically upward, the work done by your hand gives it kinetic energy. As the ball rises, it loses KE and gains PE. When it comes to a stop at its highest point, it has only PE. As it start to fall, the PE is converted back into KE. If there were no air friction, when it reached the level where it left your hand, it would have the same KE again.