How Long Is A Microcentury

How many minutes are there in 1 microcentury?

~ 53 minutes, which approximately matches the length of this grade.

LINEAR MOMENTUM

Although Newton had the selection of writing downwardly his Second Law of Motion as the familiar , he chose to practise information technology as: .

Arose from concept of a conserved quantity which he thought of every bit the "quantity of motion". Named it (linear) MOMENTUM. Annotation p is a vector!

Oppositely directed momenta tin can cancel; relative motion needs to exist considered:

Momentum of a baseball thrown at (very) loftier speed s : v = 46.3 chiliad/s; g = 0.xiv kg. Find p as it left pitcher's manus: p = mv = half-dozen.five kg grand/s, due s.

Now suppose a concoction hits information technology back towards the bullpen at 50 m/s. Decide the final momentum and the change in momentum.

Outset what happened? Bat exerts a force on ball for a few ms:

Magnitude of p' = 50 chiliad/due south 0.xiv kg = seven.0 kgm/s; direction: north.

Magnitude of D p = 13 kgm/s; Direction of D p : north. (large changes when direction of motility reversed).

And then N2: is read: rate of modify of momentum with respect to time is the cyberspace practical force, F ext .

The NET forcefulness exerted on a trunk = the resulting change in momentum / time interval the force is practical.

In collisions, D t = collision time.

If yous desire to understand this equation: play POOL!

("Dad, Honest!! My physics professor told be to go play pool!")

Note that . Left hand side chosen the "IMPULSE". Although we are assuming Fext constant during a process, if nosotros accept a variable F vs time:

Implications: To go a desired D p, can employ |F| and/or D t to achieve.

If you lot bring object to rest (rel. to globe) or if initially at residual, so F from that instant controls DIRECTION of 5 (p). (golf game brawl, tennis ball, thrown objects). Times of practical F vary in sports:

For instance: once ball leaves (bat-foot-racket-paw) then mg takes over (or in isolated space or on a flat frictionless surface, N1 takes over).

To slow the Luner Excursion Module, falling towards the moon's surface:

Conservation of Linear Momentum

Originally based on experiment; stated first by Descarte --antiseptic by Newton:

When the resultant of all external forces acting on a system is zero, the linear momentum of the system remains abiding.

Comes about because in the isolated organisation, if A pushes on B to alter the momentum of B, and so by N3, B pushes on A to change the momentum of B by an equal and reverse amount.

Often can get a isolated organisation by including more of the environment (surroundings).

TWO OBJECTS: If m one with initial velocity collides with m 2 with initial velocity , and then:

(one)

f == concluding, i == initial. The arrow over the means that the direction as well as the magnitude of the velocity must exist considered.

Consider two astronauts, Myra and Mervin in isolated infinite with a Medicine Ball.

wpe2E.jpg (37367 bytes)

Taking Myra, Mervin, and the ball as the arrangement, p=0 always. All forces are internal (pushing and catching the ball). Consider the ball as the system: forces change p all the time. Ball is not isolated.

Taking the (Moving Brawl and Mervin) (2nd - 4th drawing): isolated, p = 10 kgm/s. Until Myra catches the ball and pushes it back, the ball and Mervin are isolated and concerve momentum.

Consider "Explosion" on Air Rails

At t = 0, v i = v 2 = 0; We fire thread. Spring stretches pushing with equal strength on both masses (F 1 = -F 2 ). From Conservation of Momentum:

If grand 2 > 1000 ane , then lighter mass m 1 moves away faster than heavier one, thousand 2 . True of 3D Explosion (Star Wars), also.

Totally Inelastic Standoff: m 2 initially at rest:

Stopping Things

When objects have p, to bring to rest ( D p = p) requires application of an impulse: F D t = p.

To preclude harm (injury), F < F max .

Therefore, to reduce F, INCREASE D t!!!!

Safety Nets, Pole Vault Pit

Baseball Gloves

Boxing Gloves

Running Shoes

Helmuts

Shoulder Pads

Bumpers

Air Numberless

In front end collision, without seatbelt, you go a projectile:

wpe33.jpg (21686 bytes)

Longer contact time means reduced bear upon force -- less likely cause an injury.

Inflation of Bag: Must occur during deceleration of car and before head reaches wheel/nuance (typically 0.05 s). Sensors detect abrupt deceleration, send signals to a processor that looks for simultaneous warnings -- closes a switch that runs LARGE Electric current in an igniter in the air bag. NaN 3 (sodium azide) powder explodes (decomposes rapidly) to yield tons of Due north ii . Entire sequence takes only 0.025 s! Nylon bag dusted with corn starch to prevent sticking -- acts every bit a lubricant, to reduce time.

Usual warning: Airbags only protect you lot for forward collisions (front end). ALWAYS Clothing YOUR SEAT BELTS!

Two body collision with free energy conservation adds this equation:

(ii)

HOLDS ONLY IF Collision IS TOTALLY ELASTIC.

In one dimension, can solve for v 1f and v 2f :

Special Cases:

m 1 = m 2 = m; five 2i = 0

(direct striking on pool table)

m 1 = m 2 = m; v 2i = -v 1i

thousand two = infinity, v 2i = 0 (Brick Wall):

Ballistic Pendulum

A projectile of mass g and velocity 5 is fired into a big mass M suspended similar a pendulum.

Totally Inelastic Standoff; momentum conserv.: .

Nosotros assume m comes to rest before k+M starts moving; good approx. for M>>m.

But equally soon as (m+M) starts to motility, the string(s) crusade (m+M) to lift to a maximum height, h. Energy conservation for this motion yields:

A 2000 kg Cadillac limousine moving east at 10 thou/s collides with a 1000 kg Honda Prelude moving west at 26 m/s. The collision is completely elastic and takes identify on an icy (frictionless) patch of road. Detect the mutual velocity of the cars after the standoff and the fractional loss in kinetic energy.

SOLUTION: Label initial velocities with the alphabetic character "u" and the mutual last velocity as "". No friction on the route surface and gravity acts only in the vertical direction, so there are no external horizontal forces, where system = both cars. Therefore, momentum conserved:

m 1 u 1 - thousand two u 2 = (m ane + m 2 )V

(bold V is in +10 direction (to correct).

Solve for Five:

wpe3E.jpg (9561 bytes) Minus sign ways that the cars actually go in the -x direction or to the left subsequently the standoff.

Fractional change in kinetic energy:

(tremendous loss!!). The fractional change is:

Nigh all of the energy associated with the motion of the cars turns into some other form of energy, i.e., deforming the cars since automobiles are designed to absorb energy in fenders and front body parts during a collision.

Heart of Mass

For a collection of masses hooked together rigidly, we can find a indicate, the Middle of Mass (c.m.), where all the mass (Grand) can exist idea of as concentrated, every bit the object translates according to N2:

Southward F = ma c.m.

The c.m. moves as though all mass were concentrated in that location,

acted on by resultant of external forces.

Consider a distribution of 2 masses continued by a massless bar:

Suppose we apply force F at the bespeak which nosotros call the c.m. Then we want m 1 and m 2 to both advance with a = F/(thousand 1 + m 2 ) and the bar will not rotate. This will occur when:

Notation: m 1 (x c.m. - x i ) = m 2 (ten 2 -10 c.m. ) or m ane a(x c.chiliad. - 10 1 ) = m two a(ten 2 -ten c.1000. ); ways there are no torques about c.1000., so bar will not rotate. Therefore when F practical at c.chiliad., the system (m 1 ,yard 2 ) moves with acceleration given by

F=1000total a

For one D mass distributions:

Collection of masses in two dimensions:

and

In gravitational field, all m i feel m i chiliad force; If nosotros apply a strength F = M total yard at c.m., object will remain at remainder and will non rotate. (we then call c.m. = c.g. ---center of gravity).

Also, if you support an object at a betoken not = to c.m., object volition rotate until c.grand. is direct below point of support. Tin utilize to discover c.thousand. of 2-D objects by hanging from ii points. If c.yard. is below point of support, stable.

c.one thousand. can lie outside body -- due east.g., balancing forks, coat hanger on head.

If you launch objects with capricious forces, they rotate + translate. They rotate about c.m.; c.m. moves equally if all mass were concentrated at c.yard. (Throw a tennis racket or a wrench; your roommate).

Explosions of projectiles: c.yard. keeps moving uneffected; fragments conserve momentum (p o = 0 west.r.t. c.m.).

Suppose two equal parts, tail part shoots straight down:

c.m. travels along parabola that 2m would have followed.

Cylinder on paper:

You lot pull newspaper, cylinder rolls backwards on paper; just relative to table F accelerates cylinder to right. (strength on cylinder = f friction which is to the right).

ROCKETS

Propelled by ejection of mass, unremarkably in course of gas. (they practise non move by pushing on basis or on atmosphere). Works anywhere.

1920 New York Times editorial brash Robert Goddard to give up thoughts of space travel -- "even a schoolhouse male child knows that rockets plainly cannot fly in space considering a vacuum is devoid of annihilation to push on." WRONG!!

Information technology is the relative velocity of the ejected mass (relative to the rocket) that determines the Forcefulness pushing the rocket [CALLED THE THRUST!]

If D M is the amount of mass existence ejected in time D t, and this is ejected (relative to the rocket) with velocity V ex ,

and so we can testify:

A Centaur Rocket shoots hot gas from its engine at a charge per unit of 1300 kg/south (this is D Yard/ D t). V ex = 50,000 thousand/s (These are BIG numbers)

F thrust = 65 MN (this is about 7000 tons of force).

Note that equally time goes on, rocket gets lighter; therefore acceleration increases with time (for constant D M/ D t).

Contrary thrust: Used to decelerate:

You have all experienced this when landing in aeroplane: Jet engines (or props) "reversed": flow of air deflected 180� by cowls or props rotated to "blow forwards". Generates Braking Impulse (Ft) -- bike brakes could not generate nearly as much forcefulness.