Momentum, Work, Energy

Momentum: The product of a particle’s mass and its velocityImpulse: Change in momentum caused by a net force (note must consider sign change in velocity before and after collision). Product of the force and time. Know how to define and state relation to momentum.Area under a force-time graph used to find maximum force.Use Ft=p to find average force when momentum and time given.When calculating change in momentum, note sign of velocity, hence usually the magnitude of the initial and final momentum will add up due to different signs.Law of Conservation of Momentum: The total momentum of a closed system is constant provided no external resultant force acts on it.(Know how to derive this equation and explain using Newton’s 2nd and 3rd Laws of Motion)Elastic collision: After collision, two bodies move separately, total kinetic energy and total momentum is conserved.To verify if collision is elastic, calculate initial and final kinetic energies.Perfectly inelastic collision: After collision two bodies move as one, total momentum is conserved but not total kinetic energy (some lost in the form of heat and sound)Inelastic collision: Same as above, just that both bodies may not move together as one (but in same direction)Use formula for total momentum before collision = total momentum at collision. However since kinetic energy not conserved, must considered total energy at collision = total energy after collision where total energy = PE + KE. (e.g. ballistic pendulum, car accident)Falling ball: Momentum is conserved because have to consider earth and ball as a system. The earth actually moves towards the ball as it falls but the mass of the earth is large and therefore no observable movement.For boat moving from land into water tank causing water to move: Calculated gain in KE of water will be less than loss in KE of boat. Momentum has been conserved but not KE. Not all the water will move forwards as some water will be displaced sideways. Hence not all the KE in the forward direction is conserved.Explain how Newton’s 3rd law leads to the concept of conservation of momentum in the collision between two objects in an isolated system:Before and after collision, no forces acting on the objects. According to Newton’s 3rd Law, when the two bodies are in contact they exert equal and opposite forces on each other. Thus net force on the two balls is always zero, no change in momentum of the system and hence momentum conserved.For stationary helicopter, blades exert a force on the air, force a column of air to move downwards, and by Newton’s 3rd Law the air exerts an equal and opposite force on the blades. If this force equals the weight of the helicopter, net vertical force on the helicopter is zero and the helicopter remains stationary. Work: The net force multiplied by the displacement in the direction of the net force (the energy that is transferred or used).1 Joule of Work: When a net force of 1 newton moves through a displacement of 1m in the direction of the net force. Energy: The capacity to do work.Area under force-distance graph is equal to work done.Types of energy: Chemical potential energy in food and fuel, nuclear energy in atomic bombs and nuclear reactors, radiant energy in EM wavesKinetic energy: Energy possessed by an object due to its motion.Potential energy: Energy stored in a body as a result of its position, shape or state.GPE: For a body near surface of earth at height h, the work done to raise the body to height h from a reference level.Principle of Conservation of Energy: Total energy in a system remains constant. Energy cannot be created or destroyed but converted from one form to another.(Always note effects of friction and air resistance) Total IE + Energy supplied/work done = Total FE + work done against friction.Efficiency: The ratio of the useful energy output to the energy inputPower: Rate of work done/energy change.No Work done when Force is perpendicular to displacement e.g. in circular motion, carrying a mass and running horizontallyBall falling on elastic spring: KE loss + GPE loss (derived from change in spring height) = Elastic PE gained by springMain energy transformation in an electric motor: electrical –> thermal, kinetic –> electrical

New Page