Review CM 8.01 PDF

Page 2 The difference between speed and velocity is that speed is the magnitude of velocity another word , if there is a velocity without a vector it is speed -The **average velocity** is change in displacement divided by change in time \- **instantaneous velocity** is the derivative of displacem...

Page 2 The difference between speed and velocity is that speed is the magnitude of velocity another word , if there is a velocity without a vector it is speed -The **average velocity** is change in displacement divided by change in time \- **instantaneous velocity** is the derivative of displacement [\$\\frac{\\text{dx}}{\\text{dt}}\$]{.math.inline} with respect to time Velocity is science sensitive while speed is not look in example page \#3 -The **uncertainty** could be measured in many methods [*measurement* ± *uncertinty*]{.math.inline} 1. in ratio case With same uncertainty as in Page 2 for instance [\$\\frac{h1}{h2} = \\frac{\\text{integer}\\text{\\ of\\ h}1 + \\ \\text{uncertinty\\ }}{\\text{integer\\ of\\ h}2\\ - \\ \\text{uncertinty\\ }}\$]{.math.inline} 2. In number as an example In Page 4 we divide the and uncertainty by number of measurement and we will get the relative error in percent - The average acceleration is change in velocity divided by change in time. Page 4 i. we will increase because angle of [*α*]{.math.inline} increase ii. Sign of average acceleration and velocity depend on how we define the increases of X - **Impact time** is the duration of time that the object take To stop completely after collision i. It\'s different with different of objects look page 4 - **Instantaneous acceleration** is the derivative of velocity with respect to time [\$\\frac{\\text{dv}}{\\text{dt}}\$]{.math.inline} - In example in page \#5, When we have the displacement and he asked for the when X = 0 we could use the Quadratic formula to find it we will have t answer and we could do it also with velocity To find when v = 0 - Gravity acceleration is independent of mass, speed, chemical composition, size, shape of objects assuming that we have no air drag - In vector the 3D problem often become 2D Problem - Page 8,9 motion in my direction is independence of X direction this so through an objects in certain angle i. Through ball and we move in X direction with sane constant velocity of the ball then we will catch the ball look example In Page number 9 - **Uniform circular motion** is motion of body travelling at constant speeds across circular route page 13 i. Speed not changing but velocity victor is changing and always will be pointing toward a centre of circle ii. **centripetal acceleration** is Acceleration Victor pointed toward center of the circle and it will be linear in r since it is v(t) iii. - The relation between centrepetal acceleration And perceive gravity is that the pull or push will be opposite direction of perceived gravity i. for instance, when someone stand on surface he will feal push from the floor up so the perceived gravity will be down look at graph and page 15 ii. faster I rotate stronger I will pull and stronger will be the perceived gravity - In Page \#16 graph showed tube rotated around axis With water inside i. The gravity effect in side is stronger than the up ii. liquid will be vertical and the light particle become heavier **why light particle doesn\'t fall to bottom?** Due to temperature the molecule of particle have chaotic motion Known as **\"Thermal agitation\"**, later the molecules act with the small and light particles and that\'s the reason that keep it doesn\'t fall - **Galileo\'s initial law or first Newton law** is body at rest remain at rest and body in motion continue to move at constant velocity along straight line and less acted upon by external force **when the first law work?** When frame of reference (inertial) which is frame that there are no acceleration of any kind First law holds only in inertial frame **Can Newton law be proven?** No it is impossible to be sure that your frame of reference is without any acceleration - **2nd Newton law** is force action on body gives it an acceleration which is in direction of the force and have magnitude given by \"ma\" i. it\'s hold an inertial reference frame ii. When we approach speed of lights new too low will not valid anymore and Einstein theory of special relativity will be taking place - **3rd Newton law** is if one object exerts force on other the other exerts same force in opposite direction \ [**Action** **=**  **−** **Reaction**]{.math.display}\ i. if I push wall the wall will push back in opposite direction with same force ii. It hold whether objects are moving or accelerative it\'s called connect force Means it\'s hold in any frame of reference not only in inertial - **decomposition** is for instance velocity objects can be decomposed into two components **along X&Y axis** - **How to measure tension?** **Look page 22** - **what is weight?** It is force from surface scale on the body - **Freefall** insulation in which object move only under influence of gravity - Weight independence by tension **string** - String cannot be negative T page 25 - In freefall the object doesn\'t have weight Like when we jump from top of disc when we are in air between the disc and ground the velocity will be downward and we are weightless and when he hits the ground it must be an acceleration upward to make v = 0 as a result of that our weight will be 3.5g times the normal - [*μ*]{.math.inline}~s~ is the static friction coefficient is to break it loss to get it\'s going - [*μ*]{.math.inline}~k~ is the kinetic coefficient is to keep it going - [*μ*]{.math.inline}~s~ is independent of mass and surface **why race cars have word tiers?** EX, if there is a car or track an angle and it\'s increase [*μ*]{.math.inline}~s~ for rubber on concrete equal 1 and [tan 45 = 1]{.math.inline} So track and the car will start slights in angle the width of tyre nuts important - In fraction to determine in which direction it will accelerate there will be 3 case: (looking page 28 inside the red box on the left) i. acceleration up and friction force is down (At the moment of the starting accelerates) which means that M2 is bigger than M1 ii. acceleration downward and the fraction force upward iii. If neither 1 nor 2 it won\'t move so a = 0 So when we solve any problem we test the condition one if it didn\'t work then we test condition 2 if they don\'t work it will be condition 3 - Hook\'s law Is state that force needed to extend or compress a Spring is directly proportional to the displacement of spring from it is equilibrium states Whenever the linear relation between F&X holds it will called Hock\'s law When x + Direction \--\> F -Direction end opposites - How to measure spring constant? Using gravity see page \#32 - The ideal case I. Hock\'s law must hold II. Frictionless III. Messless - The period and angular velocity is independent of amplitude and Phi Period of osculation is independent of amplitude of objects - **Small angle approximation** is method where sine and cosine functions for small angles can be approximated by the angle itself in radians For spring, if extended it over Certain distance then there is certain force and it is independent we put at the end of spring If mass doubled the fixed force will give us half acceleration in osculation if the mass increase the frequency go down in other words, if double the mass the fixed force will give us half acceleration and FXL edition go down the period of escalator goes up for pendulum, if we double the mass the vertical components of the tension doubled the restoring force also doubled and acceleration and period remained the same - **Restoring force** is act on an object to bring it back to the equilibrium position when displaced from that position - \ [*f* =  − *kx*]{.math.display}\ - If k is high spring stiff meaning if we give a small extension meaning that spring force is huge acceleration in given mass is high due to high accelleration. Will be short - if there is pendulum in order a space it can\'t swing and it will be steady while spring will move - period of escalation is independent of mass of the object - Work is measure of energy transfer that occurs when an object is moving over distance by external force at least parts of which is applied in direction of displacement - **Work-energy theorem** is work done on an object is equal to the change in it is kinetic energy, a harmony between efforts and transformation It has three cases: I. +W -\> Ke Increase II. W\ Ke Decrease III. W=0 -\> No change EX, when we put bag on surface Work \"-\" -\> Gravity \"+\" when we hold it Work \"+\" -\> Gravity \"-\" - **Conservative force** is whenever the work that is done by force in going from one point to another is independent of path it is only determined by starting an endpoint Gravity is conservative force - **potential energy** is energy stored in object due to it is position relative to a force such as gravity or spring. it represents the capacity of object to do work **gravitational potential** energy is depend on an object height and mass and gravitational field as definition in Page 40 is at A points p is work I have to do to bring that mess from Infinity to that points p - mechanical energy yes sum of an object\'s kinetic energy and potential energy and it is represent the total energy available to an object for performing work a force is conserved to force spring force is conservative but friction is not - **Drag force** is when we move an object through a medium gas or liquid and it\'s the **depend** on size, shape of the medium and speed of an object - **it will be divided into regions:** i. region 1 viscous term (like oil, honey, water) ii. region 2 pressure term (like air) iii. we must note that in a space object it\'s nearly exists so we neglect it - **Critical velocity** is a specific speed at which system undergoes a significant change in its behaviour - Air drag is resistance encountered by object moving through the air - **Turbulence** is the main cause of slowdown in region 2 - Look example in page 44 and explanation in the page 45 - In Page 46 distance between 0 to P take longer time then P to S and that\'s because from 0 to P the air drag and gravity decelerate however from P to S the gravity will accelerate while air drag causes decelerate - summarising the previous point. In general, air drag decelerate the object - The gravitational force is opposite direction than increasing value of potential energy Page 48 \ [\$\$\\frac{\\text{du}}{\\text{dx}} = - F\_{x}\$\$]{.math.display}\ i. released object with v = 0 it will allow to move toward lower potential energy because force drive it to lower potential energy - We know potential energy you could know the force And if we know potential energy as a function of space we could find 3 components of forces in three direction - Look bottom of page 49, a stable point the derivative of potential energy versus X is **positive** at unstable point the derivative of potential energy versus x is negative - **Simple harmonic motion** is the osculation of the objects in equilibrium - We apply the mechanical energy because at x it has a speed V and because of spring force is conservative force. - We apply the principle of mechanical energy when the force acting are conservative and non conservative force are negligible. - The osculate happened in **potential well** **potential well** is curved potential energy profile where a particle escalates within it Look page 51. - Since force always perpendicular to direction of motion and [*w* = *F*.*dr*]{.math.inline} Neither tension nor normal force does any work - Mechanical energy is conserved because gravity is conservative force - The total energy when we leave the earth with [*v*~esc~]{.math.inline} I. [*E* ≥ 0]{.math.inline} unbound orbit II. E \< 0 bound orbits (no escape) - Power is work done in certain amount of time [\$\\frac{\\text{dw}}{\\text{dt}}\$]{.math.inline} (j/s or watt) - If F perpendicular to velocity vector [*p* = 0]{.math.inline} - page 56 when we drive a bicycle with constant velocity, my force is cancelling the drag force but when we push the pedals it Push back and it cause no net force on bike - **internal force** is horses that act within system or an object and they do not change the centre of mass motion of system. Like example above - **external force** is 1st that act on system from outside the system boundaries and they can change the motion of the system. Such as drag force, friction - The motion of bike In Page 56 caused by friction force - Calories is energy needed to increase one gramme of water by 1°C - Form of energy: i. electric energy ii. chemical energy like gasoline burning, fossil fuel iii. chemical energy like when we move things in gravitational field iv. nuclear energy - Mechanical energy can be converted to electric energy as coffee machine - nuclear energy can be converted into heat and can be converted into mechanical energy and to electric energy - Chemical energy convert it into heat and converted into electric energy - why would we through a lightning bolt it blank for certain time? \'cause when it hits the surface the battery open circuits and it\'s activated. The mechanical energy could close the circuit causing ball blinking it\'s believed for certain time because the internal circuit has a timer - when there is a force acted upon an opposite a particle it must change its momentum - Page 60 when the total external force acting on system equals 0 the total momentum of system remains constant with respect to time \ [\$\$\\frac{dp\_{\\text{tot}}}{\\text{dt}} = \\ F\_{\\text{tot}\_{\\text{external}}}\$\$]{.math.display}\ \ [ *F*~tot~external~~ = 0]{.math.display}\ momentum of the system is conserved - When globular cluster collide, The forces involved are internal force. As long as there is no external force acting on system, The total momentum of system remains unchanged even if individual cluster may change their trajectories for fragment. - Individual stars can change their momentum due to internal forces, such as gravitational interactions with other stars; however, the total momentum of the system remains constant if no external forces act on it. - Kinetic energy can be destroyed but momentum cannot be look at example In Page 61 and 62 - **impact time** is duration over which two objects are connected during a collision or impact. It is also the time interval during which forces are exchanged between the colliding bodies - How to measure speed? Look page 63 the experiment with diode explain how based on time we could know the speed - Behaviour of centre of mass is predictable - Momentum of the centre of mass will not change - centre of mass motion in absence of external force has constant velocity - There is three kind of collision: \ [*KE* + *Q* = *KE*]{.math.display}\ Q is number Name Condition case ------------------------ -------------- -------- Superelastic collision Gain KE Q \> 0 Elastic collision KE conserved Q = 0 Inelastic collision Loss KE Q \< 0 - In case of elastic collision v~2~\' Is in the same direction of v~1~ Because second object standing still so we blow something into the second object it will continue that direction - If we move to the center of mass frame, meaning I move with the same velocity as the center of mass, the center of mass will appear stationary in my reference frame. In this frame, the total momentum of the system is zero both before and after the collision - Kinetic energy and momentum depend on my reference frame - In my reference frame, which is moving relative to the center of mass frame, the total momentum of the system is not zero - Unique property of centre of mass: In the center of mass frame, if two particles collide and stick together, kinetic energy is not conserved; some of it is transformed into other forms of energy. This type of collision is called an **inelastic collision** - We measure the velocity after the collision by apply the work energy theorem or conservation of mechanical energy - The impulse is change in momentum - Page 73, in case of objects drop to floor: I. if elastic it will fall downward and bounce up(back) with same speed \ [*I* = 2*mv*]{.math.display}\ II. inelastic such as tomato it will be only down speed not up (not bounce back) \ [*I* = *mv*]{.math.display}\ where I is impulse - V is velocity in my frame, U is relative to the Rockets \ [*v* \> *U*]{.math.display}\ Exhaust going up from my friend \ [*v* \