How countless minutes room there in 1 microcentury?
~ 53 minutes, which about matches the length of this class.
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Although Newton had actually the option of composing down his 2nd Law that Motionas the acquainted
Arose from concept of a conserved quantity which he thought ofas the "quantity of motion". Called it (linear) MOMENTUM. Note p is a vector!
Oppositely directed momenta have the right to cancel; relative motion needs to beconsidered:
Momentum that a baseball thrown in ~ (very) high speed due southern : v = 46.3m/s; m = 0.14 kg. Uncover p together it left pitchers hand: p = mv = 6.5 kg m/s, due south.
Now mean a batter access time it ago towards the pitcher at 50 m/s.Determine the last momentum and also the readjust in momentum.
First what happened? Bat exerts a force on ball for a few ms:
Magnitude that p = 50 m/s 0.14 kg = 7.0 kgm/s; direction: north.
Magnitude the Dp= 13 kgm/s; Direction of Dp :north. (large alters when direction of activity reversed).
The NET pressure exerted ~ above a human body = the resulting adjust in inert /time expression the pressure is applied.
In collisions, Dt = collision time.
If you want to know this equation: play POOL!
("Dad, Honest!! mine physics professor told be to walk playpool!")
Implications: To obtain a desired Dp, can use |F| and/or Dtto achieve.
If you carry object to rest (rel. Come earth) or if at first at rest,then F native that immediate controls DIRECTION that v (p). (golf ball, tennis ball, thrownobjects). Time of used F vary in sports:
For example: when ball pipeline (bat-foot-racket-hand) then mgtakes end (or in isolated room or top top a level frictionless surface, N1 bring away over).
To slow-moving the Luner Excursion Module, falling in the direction of the moonssurface:
Conservation of straight Momentum
Originally based upon experiment; stated an initial by Descarte --clarified byNewton:
When the result of all external forces acting on a mechanism is zero,the straight momentum of the mechanism remains constant.
Comes around because in the diverted system, if A pushes ~ above B come changethe inert of B, climate by N3, B pushes on A to readjust the momentum of B by an equaland the contrary amount.
Often can acquire a isolated mechanism by including more of the environment(surroundings).
TWO OBJECTS: If m1 withinitial velocity
f == final, ns == initial. The arrow over the
Consider two astronauts, Myra and Mervin in isolated room with aMedicine Ball.
Taking Myra, Mervin, and the ball as the system, p=0 always. Every forcesare internal (pushing and catching the ball). Consider the ball as the system: forceschange ns all the time. Sphere is no isolated.
Taking the (Moving Ball and also Mervin) (2nd - 4th drawing): isolated, p =10 kgm/s. Till Myra captures the ball and also pushes it back, the ball and Mervin are isolatedand concerve momentum.
Consider "Explosion" on waiting Track
At t = 0, v1 = v2 = 0; we burn thread. Feather stretches pushing with equalforce on both masses (F1 = -F2). Indigenous Conservation that Momentum:
If m2 > m1, then lighter fixed m1 move away much faster than heavier one, m2. True that 3D explosion (Star Wars), also.
Totally Inelastic Collision: m2 at first at rest:
When objects have p, to lug to remainder (Dp = p) requires application of an impulse: FDt = p.
To prevent damages (injury), F max.
Therefore, to reduce F, rise Dt!!!!
Safety Nets, Pole Vault Pit
In front finish collision, without seatbelt, you come to be a projectile:
Longer call time means reduced impact force --less likely reason an injury.
Inflation of Bag: should occur during deceleration the car and before headreaches wheel/dash (typically 0.05 s). Sensors detect spicy deceleration, send signal toa processor the looks because that simultaneous warnings -- close the door a switch the runs LARGECURRENT in one igniter in the wait bag. NaN3 (sodiumazide) flour explodes (decomposes rapidly) come yield lots of N2. Entire sequence takes just 0.025 s! Nylon bag dusted v corn strength toprevent sticking -- acts together a lubricant, to alleviate time.
Usual warning: Airbags only safeguard you because that forward collisions (frontend). Always WEAR her SEAT BELTS!
Two body collision with power conservation adds this equation:
HOLDS just IF COLLISION IS entirely ELASTIC.
In one dimension, have the right to solve because that v1f and also v2f:
m1 = m2 = m; v2i = 0
(direct hit on swimming pool table)
m1 = m2 = m; v2i = -v1i
m2 = infinity, v2i = 0 (Brick Wall):
A projectile of massive m and velocity v is fired into a big mass Msuspended favor a pendulum.
Totally Inelastic Collision; inert conserv.:
We i think m concerns rest prior to m+M starts moving; an excellent approx. For M>>m.
But as quickly as (m+M) starts to move, the string(s) cause (m+M) to lift come a maximumheight, h. Power conservation because that this movement yields:
A 2000 kg Cadillac limousine moving eastern at 10 m/s collides with a 1000kg Honda Prelude relocating west at 26 m/s. The collision is fully elastic and also takesplace on an icy (frictionless) job of road. Find the usual velocity that the cars afterthe collision and also the fractional loss in kinetic energy.
SOLUTION: brand initial velocities with the letter "u" andthe typical final velocity as "
m1u1 - m2u2 = (m1 + m2)V
(assuming V is in +x direction (to right).
Solve because that V:
Fractional change in kinetic energy:
(tremendous loss!!). The fractional adjust is:
Almost every one of the energy connected with the motion of the cars turnsinto part other form of energy, i.e., deforming the cars due to the fact that automobiles room designed toabsorb energy in fenders and front human body parts during a collision.
Center that Mass
For a arsenal of masses hooked together rigidly, us can uncover apoint, the center of fixed (c.m.), whereby all the massive (M) deserve to be assumed of asconcentrated, together the object translates according to N2:
SF = mac.m.
The c.m. Moves as though every mass were concentrated there,
acted ~ above by resultant of external forces.
Consider a distribution of 2 masses linked by a massless bar:
Suppose we apply force F in ~ the suggest which we contact the c.m. Climate wewant m1 and also m2 come both accelerate with a = F/(m1 +m2) and also the bar will not rotate. This willoccur when:
Note: m1(xc.m. - x1) = m2(x2-xc.m.) or m1a(xc.m. - x1) = m2a(x2-xc.m.); means there space no torques around c.m., for this reason bar willnot rotate. Thus when F used at c.m., the device (m1,m2) moves with acceleration provided by
For one D mass distributions:
Collection that masses in 2 dimensions:
In gravitational field, every mi suffer mig force; If we use aforce F = Mtotal g in ~ c.m., object will remainat rest and will no rotate. (we then contact c.m. = c.g. ---center the gravity).
Also, if you support an object at a suggest not = come c.m., object willrotate till c.m. Is straight below suggest of support. Have the right to use to discover c.m. The 2-Dobjects through hanging from two points. If c.m. Is below point of support, stable.
c.m. Have the right to lie exterior body -- e.g., balancing forks, coat hanger onhead.
If you launch objects with arbitrary forces, they rotate + translate.They rotate around c.m.; c.m. Moves together if all mass were focused at c.m. (Throw atennis racket or a wrench; your roommate).
Explosions the projectiles: c.m. Keeps moving uneffected; fragmentsconserve momentum (po = 0 w.r.t. C.m.).
Suppose 2 equal parts, tail part shoots directly down:
c.m. Travels follow me parabola the 2m would have actually followed.
Cylinder ~ above paper:
You pull paper, cylinder rolls backwards on paper; but relative totable F accelerates cylinder come right. (force on cylinder = ffrictionwhich is come the right).
Propelled by ejection that mass, generally in type of gas. (they perform not move by pushing onground or ~ above atmosphere). Works anywhere.
1920 brand-new York times editorial advised Robert Goddard to offer up think of spacetravel -- "even a school boy knows that rockets obviously cannot fly in an are becausea vacuum is devoid of something to push on." WRONG!!
It is the relative velocity of the ejected fixed (relative to the rocket) thatdetermines the force pushing the rocket
If DM is the lot of massbeing ejected with time Dt, andthis is ejected (relative to the rocket) through velocity Vex,
then we deserve to show:
A Centaur Rocket shoots warm gas indigenous its engine in ~ a rate of 1300 kg/s (this is DM/Dt). Vex = 50,000 m/s (These room BIGnumbers)
Fthrust = 65 MN (this isabout 7000 tons of force).
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Note that together time goes on, rocket gets lighter; therefore acceleration rises withtime (for constant DM/Dt).
Reverse thrust: supplied to decelerate:
You have all proficient this once landing in airplane: Jet engines (or props)"reversed": circulation of wait deflected 180� by cowls or props rotated to "blowforwards". Generates Braking impulse (Ft) -- wheel brakes might not create nearlyas lot force.