Work, Energy & Momentum

Property of a system to do work.

is energy of motion.  Objects that have mass and are moving with some velocity will have K.

K=(1/2)*m*(v^2)

Joule (J) = kg*m^₂/s²

Object is said to have a potential energy when it has a potential to do something. 

• U=mgh
• J= kg*m²/s²

is a sum of object's potential and kinetic energies.

E=U+K

energy is never created or destroyed.

E of the system is conserved in absence of friction.  The sum of a system's potential energy and kinetic energy will be constant.

Work is not a form of energy, but a process by which energy is transferred from one system to another.

W=F*d*cosθ

J=N*m=kg*m²/s2

• θ is an angle btw force and displacement vectors

Work and Heat

the rate at which energy is transferred from one system to another.

P=W/t

Watt (W) = J/s

W-E Theorem offers a direct relationship btw work done on an object by all forces and the change in its kinetic energy:

W_net=ΔK=KE_f - KE_i

• Quality of objects in motion.
• p=mv
• kg*m/s

Inertia -- the tendency of the objects to resist changes in their motion and momentum.

• Impulse is a change in momentum
• I=FΔt=Δp=mv_f - mv_i
• kg*m/s

• Where objects don't stick together. 
• E.g. Billiard balls
• p conserved:  p_1i + p_2i = p_1f + p_2f
• KE conserved: KE_1i+KE_2i = KE_1f+KE_2f

• Where objects don't stick together
• E.g. two cars crashing
• p conserved:  p_1i + p_2i = p_1f + p_2f
• KE not conserved: ΔKE_{i >} ΔKE_f

• Where objects stick together
• E.g. 2 cars crashing and becoming one.
• or two molecules colliding and becoming one (covalent bond).
• p conserved:  p_1i + p_2i = (m₁+m₂)*v_f
• KE not conserved: ΔKE_i > ΔKE_f

In all collisions

makes it easier to accomplish a given amount of work since the input (applied) force necessary to accomplish work is reduced.

The distance through which the reduced input force must be applied, however, is increased by the same factor.

Inclined planes, levers, and pulleys provide the benefit of mechanical advantage.

Is a point within the object at which all the object's mass could be represented as a single particle.

X=(m₁x₁+m₂x₂+....)/(m₁+m₂+...)