Work And Energy

Front 1

Conservative Force

Back 1

Path does not matter in computing work (only use end points)

Front 2

Vector Dot Product of A*B

Back 2

A·B = ||A|| ||B|| cos(Θ)

Front 3

Vector Interpretation of Work

Back 3

Integral of {Force · ds}
(ds is a small piece of the path)

Front 4

Work-Energy Theorem

Back 4

⌂Ke = Net Work

Front 5

Energy

Back 5

An object's capacity for doing work

Front 6

Gravitational Potential Energy (very close to the Earth)

Back 6

U = mgh

Front 7

Elastic Potential Energy for a Spring

Back 7

U(x) = (1/2) kx^2

Front 8

Is the spring force a conservative force?

Back 8

Yes, the spring force is a conservative force

Front 9

Work-Potential Energy Relationship

Back 9

Work = -⌂U

Front 10

Conservation of Energy

Back 10

At any given point:
Ke + Us + Ug = Constant

Ke = Kinetic Energy
Us = Potential Spring Energy
Ug = Gravitational Potential Energy

Front 11

Classical Turning Points

Back 11

Any point on a Potential Energy Graph at which Ke = 0 (that is, U = Etotal)

Front 12

Relationship between Force and Potential Energy

Back 12

F (x) = - dU(x) / dx

Front 13

Gravitational Potential Energy far from the Earth

Back 13

U(r) = -GMm / r

Derived from the fact that Gravitational Force =
-GMm / (r^2)
We know -dU/dx = F
Integral of -F = -GMm / r

Front 14

Power

Back 14

dW/dt OR dE/dt

Unit = Watt = Joule/second

Front 15

Vector Representation of Power

Back 15

P = F · V

Front 16

Power required to accelerate a car of mass m:

Back 16

P = m*v*a

Front 17

Energy dissipated due to air drag for a car of mass m

Back 17

(1/2)C A p v^3

C = constant
A = Cross-sectional area
p = density
v = velocity

Front 18

Formula for Wind Power

Back 18

P = 1/2 E*p*A*v^3
Know P ~ v^3
E ~35-50% (efficiency)

Front 19

Why are wind turbines not 100% efficient?

Back 19

Would require all air that passes through the system to lose all Ke (impossible). Hence only a portion of the air's Ke is converted.

Front 20

Formula for Hydro-power

Back 20

P = (⌂V/⌂t)pgH

Know P ~ (⌂V/⌂t)
(P is proportional to flow rate)

Front 21

Impulse

Back 21

Area beneath the Force Time graph

Units = Newton-second (same as linear momentum)

Front 22

Linear Momentum

Back 22

p = mv

Front 23

Impulse-Momentum Theorem

Back 23

⌂p = Sum of Impulses

Front 24

When two particles interact, what is the magnitude of the impulse of particle A on B and particle B on A?

Back 24

They are equal in magnitude and opposite in direction

Front 25

Inelastic collision

Back 25

Objects collide, stick together. Energy is lost. Total velocity of system is decreased.

Front 26

Elastic Collisions

Back 26

Energy is conserved: a short, sharp, "bounding" collision.
Speed of approach of the objects = speed of separation of the objects

Front 27

Thrust force for a rocket

Back 27

F = Velocity (exhaust) * d(mass fuel) / dt

Front 28

Rocket velocity equation:

Back 28

⌂v = v(exhaust) * ln(Mass(initial)/ Mass(final))

Front 29

Rotational Kinetic Energy

Back 29

Ke = 1/2 I w^2

Front 30

Parallel Axis Theorem

Back 30

Relates moment of inertia of an object about two different parallel axes, one through the CM:

I(axis) = I(cm) + Md^2

Thus we see that the axis through the CM has the lowest possible moment