Energy

A property or characteristic of a system to do work / make something happen

Kinetic Energy

The energy of motion

Objects with mass and some form of velocity will have:

Kinetic Energy

Kinetic Energy Equation

KE = ½mv^{2}

The SI Unit for Kinetic Energy is:

Joules (J)

If velocity doubles, kinetic energy will:

quadruple (assuming the mass is constant)

Potential Energy

An object that has mass and the potential to do something.

Potential Energy Equation

PE = mgh

Total Mechanical Energy is:

The sum of an object's potential and kinetic energies.

Total Mechanical Energy (E) Equation

E = PE + KE

The First Law of Thermodynamics states:

Energy is never created or destroyed. It is merely transferred from one system to another.

When the work done by nonconservative forces is zero (when there are no nonconservative forces acting on the system), the total mechanical energy of the system:

remains constant. (E = PE + KE = Constant)

When nonconservative forces such as friction and air resistance are present, total mechanical energy:

is not conserved

Work Done by Nonconservative Forces (W') Equation

W' = ΔE = ΔKE + ΔPE

The work done by nonconservative forces such as air resistance and friction is exactly equal to:

the amount of energy 'lost' from the system. NOTE: the energy was not 'lost', it was just transferred out of the system and into another.

Mechanical Energy is conserved when:

No nonconservative forces (friction, air resistance, etc. are present).

Work is:

a process in which energy is transferred from one system to another when something exerts forces on or against something else.

Work (W) Equation

W = FdcosΘ

(F = force applied; d = displacement through which the force is applied; Θ = the angle between the applied force vector and the displacement vector)

In the Work equation, Θ is:

the angle between the displacement and force vectors

Power

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

Power (P) Equation

P = W / t (where W = work and t = time)

SI Unit of Power

Watts (W)

The Work-Energy Theorem states:

the net work done on or by an object will result in an equal change in the object's kinetic energy.

Work-Energy Theorem Equation

W_{net} = ΔK = K_{f} - K_{i}

Momentum is defined as:

a quality of objects in motion. It is defined as the product of an object's mass times its velocity. Therefore, it is a vector quantity.

Momentum (p) Equation

p = mv

(where m = mass and v = velocity)

For two or more objects, the total momentum is equal to:

the vector sum of the individual momenta

Inertia

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

Impulse is defined as:

the change in an object's momentum. It is a vector quantity.

For a constant force applied through a period of time, impulse and momentum are related by this equation:

I = FΔt = Δp = mv_{f} - mv_{i}

(where I = impulse, t = time; p = momentum; m = mass; v = velocity)

The longer the time of change in momentum (Impulse), the smaller the:

Force necessary to achieve the impulse. (Example - Crush zones in cars. The longer amount of time the car crushes, the smaller the force felt on the occupancy zone by the change in momentum - the change in momentum occurs over a longer period of time, and thus the force felt is smaller)

Conservation of momentum means that:

the momentum after a collision is the same as the momentum before the collision.

Conservation of momentum occurs when:

No nonconservative forces (friction, air resistance, etc. are present).

Conservation of Momentum Equation for elastic and inelastic collisions

m_{a}v_{ai} + m_{b}v_{bi} = m_{a}v_{af} + m_{b}v_{bf}

The three types of collisions for which momentum is conserved:

Completely Elestic Collisions; Inelastic Collisions; Completely Inelastic Collisions

Completely Elastic Collisions occur when:

Two or more objects collide in such a way that both kinetic energy and momentum are conserved. They do not stick together.

Conservation of Kinetic Energy in a Completely Elastic Collision Equation

½m_{a}v_{ai}^{2} + ½m_{b}v_{bi}^{2} = ½m_{a}v_{af}^{2} + ½m_{b}v_{bf}^{2}

In completely elastic collisions:

kinetic energy and momentum are BOTH conserved

Inelastic Collisions occur when:

a collision results in the decrease of kinetic energy of the system through the production of sound, heat, light, etc.

In inelastic collisions:

momentum is conserved, but the final kinetic energy is LESS THAN the initial kinetic energy

Inelastic Collision Equation

½m_{a}v_{ai}^{2} + ½m_{b}v_{bi}^{2} > ½m_{a}v_{af}^{2} + ½m_{b}v_{bf}^{2}

Completely Inelastic Collisions occurs when:

objects collide and stick together rather than bouncing off each other and moving apart.

In completely inelastic collisions:

momentum is conserved, but the final kinetic energy is LESS THAN the initial kinetic energy

Conservation of Momentum Equation for completely inelastic collisions

m_{a}v_{ai} + m_{b}v_{bi} = (m_{a} + m_{b})(v_{f})

In completely elastic collisions, what is conserved?

KE and momentum

In completely inelastic collisions, what is conserved?

momentum; KE is lost

In inelastic collisions, what is conserved?

momentum; KE is lost

Mechanical Advantage

Any device (such as an inclined plane) that allows for work to be accomplished through a reduced applied force is said to provide mechanical advantage.

Mechanical Advantage Equation

Mechanical Advantage = F_{out }/ F_{in}

(Fout = the force exerted on an object by a simple machine; Fin = the force actually applied on the simple machine)

Mechanical Advantage is the ratio of:

the force exerted on an object by a simple machine (F_{out}) to the force actually applied on the simple machine (F_{in})

Mechanical Advantage comes at the expense of:

increasing the distance over which the work is done

Mechanical Advantage: load

the load is the weight of an object (mg) in a mechanical advantage situation

Mechanical Advantage: effort

the force applied to the simple machine in mechanical advantage

Mechanical Advantage: Load Distance

the distance an object is moved by a simple machine in mechanical advantage

Mechanical Advantage: Effort Distance

In a pulley system, the length of rope that must be pulled in order to move the object the load distance. Effort distance is longer than load distance.

Efficiency of a Simple Machine Equation

Efficiency = W_{out }/ W_{in} = (load)(load distance) / (effort)(effort distance)

Efficiencies are expressed as:

Percentages

The efficiency of a machine gives a measure of:

the amount of work put into the system that "comes out" as useful work

The six devices considered to be classic simple machines:

inclined planes, wedges, pulleys, axle and wheel, lever, and screws

In an idealized pulley (one that is massless and frictionless), the work put into the system is equal to:

the work that comes out of the system. Thus, the pulley has a 100% efficiency.

Center of Mass

The point that acts as if the entire mass was concentrated at that point.

Center of Mass Equation

X = m_{1}x_{1} + m_{2}x_{2} + m_{3}x_{3} + .. / m_{1 }+ m_{2} + m_{3} ..

(where m1, m2, and m3 are the masses of three different objects and x1, x2, and x3 are there positions along the x-axis)

Center of Gravity Equation

X = w_{1}x_{1} + w_{2}x_{2} + w_{3}x_{3} + .. / w_{1} + w_{2} + w_{3} ..

(where w1, w2, and w3 are the weights of three different objects and x1, x2, and x3 are there positions along the x-axis)