Energy: Basics

Definitions

Energy - the ability to do work Work - the transfer of energy by applying a force through a distance But what is a “force”?

Position

Position - orientation and distance an object is from some origin; measurement of position requires a coordinate system If the position does not change, the object is easily found Displacement - change in position; if position is designated with the vector

r

, then displacement is D

r

Velocity

Defn. - time rate of change of displacement; is a vector quantity; SI unit = m/s Average velocity = = Elapsed time D D t

r

Instantaneous velocity = limit (average velocity) D t  0 What is the average velocity of a dragster that takes 5.5 seconds to go the 400 meters down the dragstrip?

Speed

Some books say that velocity is speed + direction. WRONG!

Average speed = Distance traveled Elapsed time Displacement = Distance traveled Displacement on racetrack is 0, while distance travelled is not

Acceleration

Defn. - time rate of change of velocity; is a vector quantity; SI unit is m/s 2 Average acceleration = D

v

D t Accelerations can occur without changing the magnitude of velocity; Ex. Object going in circle at constant rate

Newton’s First Law

Really, Galileo’s “ An object at rest, or in a state of constant motion, will continue in that state unless acted upon by an unbalanced force.” Inverse of statement is very important: if an object is acceleration, then a net force is operating on it, even if you cannot see the reason for the force.

Is there a force operating in this picture, and if so, from what direction?

Newton’s Second Law F = ma

Relates kinematic variables to dynamic ones Can measure accelerations  calculate forces Note: SI unit is newtons, English is pounds Incorrect to say that X pounds = Y kilograms Not all forces are constant What force is needed to accelerate a 1000 kg car to 5 m/s 2 ?

Newton’s Third Law

“ For every force, there is an equal and opposite reaction force.” Often misunderstood; actually means that one object acting on a second object will have the second object act on it Mule pulls on cart. Cart pulls back on mule with equal and opposite force.

“Why pull?”, says mule, if force will be negated.

Get Back To Work

Work - the transfer of energy by applying a force through a distance

W = F x d if F is constant D W = F n x D d if F varies Lifting box: F = mg Distance lifted = h W = mg x h = mgh

Work Example

How much work is done by lifting a 10 kg box 2 meters from the floor to a shelf?

m = 10 kg h = 2 m Lifting box: F = mg = (10 kg)(9.8 m/s 2 ) = 98 N Distance lifted = h = 2 m W = mg x h = (98 N) (2 m) = 196 J

Potential energy

Energy stored within the force between two objects separated by a distance; if objects are allowed to move, force is applied through distance = work done

TYPES OF POTENTIAL ENERGY:

Gravitational Chemical Nuclear

Example: Gravitational potential energy

Potential energy due to gravity

EXAMPLES:

Water behind a dam A rock at the top of a steep hill If the water or rock drops, gravity operates over a distance, thereby doing work. This work converts the potential energy to kinetic energy.

Kinetic energy

ENERGY OF MOTION

A moving object has momentum. If it hits another object, it will transfer energy to it by applying a force through a distance, i.e. work Some of the bullet’s kinetic energy is transferred to the apple during the collision Kinetic energy of falling water is converted to motion of turbines when water falls on them

Kinetic Energy (cont.)

The kinetic energy of an object depends only on its mass and its velocity K.E. = ½ m v 2 Example: A .03 kg bullet is moving at 300 m/s right before it hits an apple. How much kinetic energy does it have?

K.E. = ½ (.03 kg) (300 m/s) 2 = (.015 kg)(90000 m 2 /s 2 ) = 1350 J

1

st

law of thermodynamics

Energy may be converted to different forms, but it is neither created nor destroyed during transformations Energy from chemical bonds is converted to kinetic energy and heat (body and friction from tires)

ENERGY

Heat Amount of energy before and after transformation is the same, only the

form

of the energy has changed

1

st

Law (Contd.)

Another way to state the 1 st law is mathematically.

D

E = Q + W

This equation says that the only way to change the energy of a system is to add heat to it (Q) or to do work on it (W) Example: Can make wood hotter by applying fire or hitting

Conservation of Energy

If no external work is done on a system, or if no heat is exchanged with its surroundings, then the total energy of a system will not change, i.e. the total kinetic plus the total potential energy will remain constant Energy can be converted from one form to the other (potential to kinetic or vice-versa), but the total will remain the same.

Simple Machines

Allow for the same amount of work to be done, but with smaller forces Trade-off of using a smaller force is that the force is applied through a longer distance Box lifted straight up a height h, force supplied is F = mg Force of gravity down inclined plane is F = mg sin q = mgh/L Distance pushed up plane = L

Power

Power = = rate of energy usage t Can deliver the same amount of energy to a system using less power, but it takes a longer amount of time Our Western mindset usually screams for more power Ex. SUV’s require more powerful engines; larger homes require more powerful a.c.

How much power do you expend by climbing 3 flights of stairs (10 m) in 10 seconds?

If you have a mass of 70 kg and each flight is 5 m, then the power is P = (mgh)/dt = (70 kg)(9.8 m/s2)(15 m)/(10 s) = 1029 W