ASTB Mechanical Comprehension

Displacement

final position-initial position

Velocity

change in position/change in time

Average velocity

displacement/change in time

Acceleration

change in velocity/change in time

Vertical velocity

original vertical velocity-gravity x time

Newton's 1st law

A body at rest will tend to stay at rest, while a body in motion will tend to remain in motion, unless acted upon by an external force

Newton's 2nd law

The acceleration of an object is directly proportional to the force being exherted on in and inversely proportional to its mass. (force = mass*acceleration)

Force equals...

Mass x acceleration

Weight equals...

mass x gravity(9.8 m/s)

Torque equals...

radius x force

Work equals...

force x displacement

Power equals...

work/time

Mechanical Advantage

output force/input force

Mechanical advantage: incline

slant length/rise

Mechanical advantage: Wedge

length/width

Mechanical advantage: Screw

2 x pie x radius/length between crests

Mechanical advantage: Lever

effort distance/resistance distance

Mechanical advantage: Pulley

More amount of connecting ropes gives greater mechanical advantage

Mechanical Advantage: Wheel and Axle

Radius of wheel/radius of axle

Gear Ratio

Driving gear/ driven gear or ?:?

Momentum equals...

mass x velocity

density equals...

mass/volume

pressure equals...

force/area

Conduction

Transfer of heat through physical contact

Convention

Transfer of heat through moving fluids(steam)

Radiation

Transfer of heat through electromagnetic waves

Voltage(potential energy) equals...

current x resistance

Electric power equals...

current x voltage or voltage squared/resistance

Scaler

has magnitude, but no direction (like mass)

Vector

A value that has both magnitude and direction

Gravitational potential energy

Gravity x mass x height

When released, gravitational potential energy converts to

Kinetic energy

Pascal's Law

pressure of fluid mechanics...hydraulics

1 horsepower equals how many watts?

746

What happens as air contracts?

The air gets colder

Voltimeter?

Measures total voltage in a circuit

Hydrometer

Measures specific gravity of liquids

Micrometer

A gauge that measures small distances or thicknesses between two faces

buoyancy

the deeper you go with an inflated ball, the more difficult it is to hold it under water. the deeper you go with the same ball, the more buoyant the ball is.

when is rate of exchange faster?

it is faster through objects of greater temperature difference

kinetic energy?

energy in motion

ammeter

measures current flow in a circuit

voltmeter

measures voltage

multimeter

measures both current and voltage

metrology

the science of measurement

When air compresses...

volume decreases, density increases, temperature increases

First class lever

fulcrum in middle(scissors, pliers)

Second class lever

Fulcrum is at one end, load is in between(wheelbarrow)

Third class lever

Fulcrum is at one end, effort in between (tongs, tweezers

Moment

force*distance

Which pulleys provide mechanical advantage?

movable

Formula for gear revolutions

r(revolutions) x d (number of teeth) = R x D

Pulley mechanical advantage

number of parts of the rope that act on the load

Note about mechanical advantage:

mechanical advantage is gained by combining a fixed pulley with a moveable pulley or another fixed pulley of a different diameter

What are hydrometers?

They use floats to measure specific gravity

What is specific gravity?

the weight of a liquid compared with the weight of water. the liquid with the highest specific gravity will cause the float to rise higher in the glass tube

The lower the density of the substance...

...the farther the hydrometer will sink.

first class lever

fulcrum in the middle (scissors, pliers)

second class lever

fulcrum is at one end, load is in between (nutcracker, wheelbarrow)

third class lever

fulcrum is at one end, effort is in between (tongs, tweezers)

Which turns faster? small or big pulley?

smaller pulley will turn faster than those larger than it. it has to "keep up" and therefore turns faster.

mechanical advantage in pistons

a2 x d2 = a1 x d1

(smaller D)/(bigger D) = mechanical advantage

axe is a...

wedge, which is an inclined plane

Fulcrum Resistance Arm Info?

the farther away the fulcrum is from the resistance arm, the greater the amount of force that is required to lift the weight and the higher the resistance arm will travel

Voltimeter?

Measures total voltage in a circuit

Does electricity flow through burnt out bulbs?

No, but a voltimeter can bypass it if connected on both sides.

Series: current and voltage

current is constant in series, voltage is not

Parallel: current and voltage

voltage is constant, current is not

Voltage formula

V=IR (voltage = currentresistance)

Which circuit usually has the greater resistance?

The circuit with the greater resistance is usually in series, because it forces the current through all resistors.

what happens to the moveable pulley in a 2 pulley system?

the moveable pulley will only move up half the distance, and spin half as much as the fixed pulley

to find a necessary rpm

take number of rods on the wheel, and divide by the number of contacts per minute (for example, twice per second = 120 contacts per minute. 10 projection rods on wheel. 120/10 = 12. must rotate at 12 rpm)

Driver wheel and adjacent wheels

if a driver wheel is present, the adjacent wheels will rotate according to how close to the center the driver wheel makes contact with them. the closer to the center, the faster it will move.

Increase length of lever arm, and then increase the effort. what happens?

enable a valve to blow off at a higher pressure. move the weight further away to do this.

(if a lever causes less effort it lets its valve blow up at a lower pressure)

micrometer

sometimes known as a micrometer screw gauge. device incorporating a calibrated screw used widely in precise measurement of small distances. remember wiki pictures of how to read

how does string length affect time

the one pendulum with the longer string takes the longest to complete 1 swing

Pendulums and weight

the weight doesn't matter for swing time. if string length is the same, swing time is the same.

board in water with weights

if a board is placed in the water with 1 weight at each end, the end with the weight closest to the center will tend to float more than the one furthest from the center

bar with weights on string

if weights hang from a string attached to a bar, less pull is exerted by the weight of less weight. the length of string doesn't matter.

buoyancy

the deeper you go with an inflated ball, the more difficult it is to hold it under water. the deeper you go with the same ball, the more buoyant the ball is.

when is rate of exchange faster?

it is faster through objects of greater temperature difference

when does water flow faster?

faster through narrow areas than wider areas? think of putting your thumb on the end of a hose to make it spray...

how does narrow/wider affect amount of flow?

the same amount of water will flow through the smaller and larger part of the pipe in a given time

what happens with object on 2 scales?

if placed evenly, each scale will read half of the total weight.

4 stroke engine

intake, compression, combustion, exhaust

wheel and axle

one of six simple machines identified by renaissance scientists drawing from Greek texts on technology

wheel and axle mechanical advantage

mechanical advantage = radius of axle to handle/radius of drum (make sure to use radius)

formula for Pressure

Pressure = Force/Area

fluid pressure

if water not moving, hydrostatic pressure. deeper down, more pressure

formula for moment

moment = force x distance; moment of force is the tendency of a force to twist or rotate an object (see torque for details). important, basic concept in engineering and physics

kinetic and potential energy

potential - energy stored in an object

kinetic - energy in motion

(when you lift a heavy object, you exert energy which later will become kinetic energy when the object is dropped). the higher something is lifted, the more potential energy is produced; thus, a greater kinetic energy is produced if something is dropped

find voltage

V=I*R (find voltage drop across a circuit or single resistor)

I=Q/T

current = charge/time

direct current

flows continuously in the same direction

alternating current

periodically reverses direction

ammeter

measures current flow in a circuit

voltmeter

measures voltage

multimeter

measures both current and voltage

units for electrical theory

charge = coulomb, C

current flow = ampere, A

Power (electrical theory)

power = volts * amperes