Mechanics Iii (Pr)

Front 1

Work

Back 1

W = Fd

Work given in joules

Or:

W = Fd cosθ

Angle at which the force is applied.

WORK is NOT A VECTOR. Scalar. Has no direction.

Work can also be found by taking the area under the curve of a force by displacement graph.

Front 2

Kilowatt Hour

Back 2

The kilowatt-hour (symbolized kWh) is a unit of energy equivalent to one kilowatt (1 kW) of power expended for one hour. One watt is equal to 1 J/s. One kilowatt-hour is 3.6 megajoules

kW x hours

Front 3

Gravitational Potential Energy

Back 3

U = mgh

Conservative force.

The work done by gravity depends only on the initial and final heights, not the path the object follows.

Friction is NOT a conservative force. The path taken determines the amount of work.

Front 4

Conservation of total mechanical energy

Back 4

KEi + PEi = KEf + PEf

WITH FRICTION:

KEi + PEi + Work done by friction = KEf + PEf

Front 5

Mechanical Advantage

Back 5

Gives the factor by which a mechanism multiplies the input or effort force.

MA = Resistance Force / Effort Force

Resistant force is the force that would be required if no machine was being used (say, you lifted a block straight up)

Effort force is the force required when using a machine (lifting this same box with a pulley or on an inclined plane)

Front 6

Efficiency

Back 6

Measures the degree to which friction and other factors reduce the actual work output of a machine from it's theoretical maximum. Say, heat is lost or friction is present.

Efficiency % = Work Output / Energy Input

Front 7

Momentum

Back 7

Is a vector quantity

p = mv

Can also be found by taking the area under the curve of force vs. time.

Front 8

Impulse

Back 8

J (Do not confuse with Joules)

J = N x s

J = Δp = FΔt

So average force applied is:

F = J/Δt

Units for impulse and momentum are interchangeable.

N x s = Kg x m / s

Front 9

Elastic Collision

Back 9

Total momentum and kinetic energy are conserved.

m1v1 + m2v2 = m1V1 + m2V2

Only elastic unless stated or dealing with subatomic particles.

Front 10

Inelastic Collision

Back 10

Total momentum is conserved but kinetic energy is NOT

Energy is converted to heat and sound. Can also be deformed.

Front 11

Perfectly inelastic Collision

Back 11

Objects stick together afterwards.

Momentum IS convserved.

Loss of kinetic energy is as great as it could possibly be.

m1v1 + m2v2 = (m1 + m2)V

Front 12

Determining whether a collision was elastic or inelastic.

Back 12

Take the initial masses and velocities and plug them into kinetic energy equations. Both before and after the collision.

1/2m1v1^2 + 1/2m2v2^2

If the same amount of energy is present in both, then kinetic energy is conserved and the collision is elastic.

Front 13

Angular Momentum and Torque

Back 13

Angular Momentum (L)

L = lmv

l = length of lever arm (shortest distance between reference point and velocity. Forms a right angle)

For a circle, lever arm is always equal to the radius.

Remember torque:

t = lF

Front 14

Rotational Accelerations

Back 14

t = Ia

a = rotational acceleration. (acceleration)

I = moment of inertia. (mass)

Front 15

Force, impulse and momentum relations

Back 15

Force equals impulse over time.

F = ΔP/Δt

Front 16

Torque, and angular momentum relations

Back 16

t = ΔL/Δt

Change in angular momentum over change in time.

Front 17

Relationship between power and force

Back 17

P = Fv

Force times velocity

Front 18

Two object of different masses sit atop a incline. How do their potential energies and inertias compare.

Back 18

Different inertias and different potential energy.

(If an object has a greater mass, it will always also have a greater inertia)

Front 19

Normal Force of a Centripetal Accelerating Object (Like a roller coaster through a loop)

Back 19

At the top of a loop, there are two forces acting on a train. The normal force (N) and the force of gravity (mg)

They both point downward, so F = N + mg

Thus, N + mg =mv2 / r

Front 20

Acceleration of a projectile considering air friction.

Back 20

The projectile experiences constant, opposing air friction the entire way.

On the way up: Friction is in the same direction as gravity

On the way down: Friction is in the opposite direction of gravity.

Because acceleration (downward) is greater on the way up, it reaches the top of it's projectile quicker than it goes from top to bottom. (Because on the way down, there is a slight force acting upward)