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Momentum ConceptsMomentum (kgm/s) = mass (kg) x velocity (m/s)Assuming that no external forces (eg. friction) act during a collision or explosion, momentum will always be conserved; total momentum before = total momentum afterwards.During an explosion, for example firing a gun, the forward momentum gained by the bullet will equal the backward momentum gained by the gun, which is why guns recoil. The gun does not recoil at the same speed as the bullet as it is much more massive. An elastic collision means that the total kinetic energy is conserved, eg. gas molecules colliding with a wall; during an inelastic collision some of the kinetic energy is converted to other forms, eg. sound energy released when a cricket ball and bat collide. The momentum is always conserved.Newton's 2nd law states that: 'The rate of change of momentum of an object is directly proportional to the resultant force which acts on the object'This leads to the equation F=\(\frac{\Delta mv}{\Delta t}\) which in turn leads to the equation F = \(ma\)Impulse = change in momentum = FtThe impulse placed on an object by a wall (or another object) would be the change in momentum of the object (DIRECTION is important - momentum is a vector). It would be acting from the wall towards the object.Because impulse = Ft it is the area underneath a Force against time graph. The force of an impact can be reduced by increasing the time taken to achieve the change in momentum - this is why cars have crumple zones and air-bags. Circular MotionAs well as linear speed, v, (the distance travelled divided by the time taken) a particle moving in a circle also has an angular speed, ω, (the angle it has moved through, in radians, divided by the time).v =\(\frac{2πr}{T}\) and ω=\(\frac{2π}{T}\) which leads to the equation v=rω Because the direction of motion of the particle is always changing, it's velocity is always changing. This means the particle is accelerating (even though the magnitude of it's velocity is constant!). Because the particle is acceleration there must be a force upon it; this force is called the centripetal force. The acceleration of a particle will always be in the same direction as the resultant force on it, and as it is moving in a circle the force is toward the centre of the circle. There are two equations for centripetal acceleration:a=r\(ω^2\) and a=\(\frac{v^2}{r}\) Using Newton's \(2^{nd}\) Law, F=ma, you get two equations for the centripetal force on an object in uniform circular motion:F =\(mrω^2\) and F=\(\frac{mv^2}{r}\) The centripetal force is not a specific type of force but could be caused by the tension in a string attached to the particle or the reaction force with the inside face of a cylinder, or the frictional force between a car and the road, but the method for solving the problem is just the same. Simple Harmonic Motion Simple Harmonic Motion (SHM) is a special type of oscillation (about a midpoint) with the following characteristics:-The force on, and acceleration of, the object are always directed towards the equilibrium position. -The magnitude of the force on, and so acceleration of, the object is proportion to its displacement from the equilibrium position. The frequency and period of the motion are independent of the amplitude; so two identical pendulums will remain in phase even if they are released with different amplitudes. The motion means that energy is transferred between being kinetic and potential (the type of potential, gravitational or elastic, depends on what is causing the force). The total of these energies is constant, due to conservation of mechanical energy, as long as the motion isn't damped. When the object is in equilibrium the PE is zero, so the KE is at a maximum. When the object is at it's maximum displacement, the KE is zero and so the PE is at its maximum. This means that the object has its maximum velocity (and zero acceleration) at zero displacement and zero velocity (and so maximum acceleration) at maximum acceleration. These statements can be used to draw displacement against time graphs, velocity against time graphs and acceleration against time graphs. There are LOADS of equations to use, but these are all given on the formula sheet, it's just a matter of inputting the right numbers and using the right one. Because of the definition: acceleration is directly proportional to displacement, in the opposite direction to displacement, and dependent on the frequency of oscillation. This gives the following equations: a=-(2\(\pi\)f)^2 x

Further Mechanics

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