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FURTHER MECHANICS LINEAR MOMENTUM: Momentum = mass * velocity Momentum is a vector quantity. The principle of conservation of linear momentum states that in any interaction between bodies, linear momentum is conserved provided no resultant external force acts on the bodies. Impulse = Change in Momentum The impulse-momentum equation helps us to analyze force versus time graphs. Where F*t represents the area under the graph. Newton’s second law of motion states that the resultant force acting on a body is equal to the rate of change of momentum of the body. The following equation is helpful when thinking about things like firework rockets, where a stream of matter m/t is ejected at a speed v: F = v * (m/t) MOMENTUM & ENERGY: Work = Average Force * Distance travelled Memorize the basic formulas of GPE, KE and Elastic Potential Energy. The principle of conservation of energy states that energy is never created or destroyed, but it can be transferred from one form into another. KE = p 2 /2m The energy of both an electron and a proton that have each been accelerated through 150V will be 150eV. However, because they have very different masses, they will have very different momentums. 1eV = 1.6 * 10 -19 Joules. There are two types of collisions: Elastic and Non-elastic collisions. In non-elastic collisions momentum is conserved but some kinetic energy has been lost. The lost in kinetic energy is the gain in internal energy as energy must be conserved. In elastic collisions momentum is conserved as well as kinetic energy. One way of showing that momentum is conserved in two-dimensional situations is to resolve each of the momentum vectors after the collision into their components parallel and perpendicular to the direction of motion of the incident ball. This will show that the momentum “up” equals the momentum “down” after the collision and thus the “vertical” momentum both before and after the collision is zero. MOTION IN A CIRCLE: Angular displacement (theta) = s/r, in radians.

Further Mechanics

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further mechanicsLinear momentum: Momentum = mass * velocity Momentum is a vector quantity. The principle of conservation of linear momentum states that in any interaction between bodies, linear momentum is conserved provided no resultant external force acts on the bodies. Impulse = Change in Momentum The impulse-momentum equation helps us to analyze force versus time graphs. Where F*t represents the area under the graph. Newtons second law of motion states that the resultant force acting on a body is equal to the rate of change of momentum of the body. The following equation is helpful when thinking about things like firework rockets, where a stream of matter m/t is ejected at a speed v: F = v * (m/t)Momentum & Energy: Work = Average Force * Distance travelled Memorize the basic formulas of GPE, KE and Elastic Potential Energy. The principle of conservation of energy states that energy is never created or destroyed, but it can be transferred from one form into another. KE = p2/2m The energy of both an electron and a proton that have each been accelerated through 150V will be 150eV. However, because they have very different masses, they will have very different momentums. 1eV = 1.6 * 10-19 Joules. There are two types of collisions: Elastic and Non-elastic collisions. In non-elastic collisions momentum is conserved but some kinetic energy has been lost. The lost in kinetic energy is the gain in internal energy as energy must be conserved. In elastic collisions momentum is conserved as well as kinetic energy. One way of showing that momentum is conserved in two-dimensional situations is to resolve each of the momentum vectors after the collision into their components parallel and perpendicular to the direction of motion of the incident ball. This will show that the momentum up equals the momentum down after the collision and thus the vertical momentum both before and after the collision is zero.Motion in a circle: Angular displacement (theta) = s/r, in radians. Angular velocity is given the symbol w (omega). Angular velocity = Angular displacement / time. Velocity = radius * angular velocity. In general T = (2 * pie)/ w For all bodies or objects moving in the arc of a circle at a constant speed, the resultant force acting on them is a centripetal force, which causes a centripetal acceleration. Newtons first law applies when an object moves at a constant speed along an arc. Newtons second law applies when we are talking about centripetal acceleration. Centripetal acceleration is inwards, perpendicular to the tangential velocity. Centripetal acceleration = v2/r = rw2 F = m * (v2 / r) When a person feels weightless, there is no reaction force- the only force acting on them is their weight.