Topic 4 – Momentum, energy, work and power • • • • • • • •
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STOPPING DISTANCES Stopping safely: When a driver sees a problem ahead, the car travels some distance before the driver reacts and steps on the brakes – this is called the ‘thinking distance’ Once the driver has stepped on the brakes, the car will travel some distance before it comes to a complete stop – this is called the ‘braking distance’ The overall ‘stopping distance’ for a car = thinking distance + braking distance Factors affecting stopping distances: Note: make sure you realise that some factors affect just the thinking distance, some just the braking distance, and some affect both 1. Person’s reaction time (i.e time it takes to respond to danger): o The slower a person’s reaction time, the longer the thinking distance o Tiredness, illness, or taking drugs or alcohol can all slow down reaction times 2. Speed of the vehicle: o The faster the vehicle is travelling, the longer both the thinking distance and the braking distance 3. State of the car’s brakes and road conditions: o For a car to come to a stop there must be friction created between the car’s tyres and the road… § the more friction between the tyres and the road, the smaller the braking distance o The amount of friction between the tyres and the road depends on: § the condition of the car’s brakes (the better the brakes, the more friction they createàshorter braking distance) § condition of the road surface (e.g if the road is wet or has loose gravel, less friction is createdàlonger braking distance) o Note: due to longer braking distances in wet conditions, drivers should leave more of a gap between their car and the car in front when it is raining 4. Mass of the vehicle: o If a vehicle has more mass, more force is needed to make it slow down o àthe heavier the vehicle, the longer the braking distance MOMENTUM Momentum is a measure of how strongly something is moving… o momentum (kg m/s) = mass (kg) x velocity (m/s) o I.e the heavier the vehicle and the faster it is travelling, the greater its momentum E.g what is the momentum of a monster truck (mass = 4500kg) when travelling at 12m/s, in an eastward direction? o Momentum = 45000 x 12 = 54,000 kg m/s east Momentum has a size and direction so is a vector quantity: o àwhen giving an answer, you should state not only the amount of momentum an object has (the ‘size’) but also the direction of that momentum (which will be in the same direction as the velocity) Conservation of momentum: When a moving object collides with another object: o their masses are added togetheràtheir combined speed will be slower
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o However, the total momentum of both objects is the same before the collision as it is after the collision - this is known as ‘conservation of linear momentum’ E.g:
Before collision: o Object on the left has a momentum = 15 x 4 = 60 kg m/s to the right o Object on the right has a momentum = 0 x 2 = 0 kg m/s After collision: o Combined objects have a momentum = 10 x 6 = 60 kg m/s to the right àthe combined momentum of the objects before and after the collision is the same This demonstrates that when objects collide, momentum is conserved (i.e it is transferred to the other object without any being lost) MOMENTUM AND SAFETY When travelling in a car, passengers are going at the same speed as the car If a car brakes suddenly, there’s a rapid change in momentum, and a strong force is applied to the passengers - this can result in serious injury (e.g passengers can smash their heads against the windscreen) The ‘rate of change of momentum’ (i.e the speed at which the momentum of an object changes) is equal to the force applied to the object…: o The rate of change of momentum = change in momentum / time taken for that change o àforce (N) = change in momentum (kg m/s) / time taken for that change (s) o E.g what is the force needed to change a cyclist’s momentum by 24 kg m/s in 4 seconds? § Force = 24 / 4 = 6 N So in a car crash…: o the quicker the rate of change of momentum (i.e the quicker the passenger’s momentum decreases to 0), the more force applied to the passengersàthe more likely the passengers are to get hurt o àsafety measures in cars try to reduce the rate of change of momentum of passengers (i.e they try to increase the time it takes for the passenger’s momentum to decrease to 0) so that force applied to the passengers is smaller Note: the ‘rate of change of momentum’ is basically the same as saying the ‘rate of change of velocity’ because the time it takes for velocity to decrease to 0 is the same time it takes for momentum to decrease to 0 (momentum = velocity x mass) o Indeed, equation above can be re-written as…: § force = [(final velocity x mass) – (initial velocity x mass)] / time § F = (mv – mu) / t Vehicle safety measures:
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1. Seat belts: o In an accident, seat belts stretchàpassenger’s velocity is slowed down more gradually o àit takes longer for passenger’s momentum to be slowed to zero (i.e the rate of change of momentum is reduced) o àforce applied to the passengers is less o àreduced chance of injury However, in high speed accidents, the force is so great that the seat belt by itself could still cause injury…à 2. cars are also fitted with airbags - these work in the same way as seat belts, reducing the rate of change of momentum 3. Cars also have crumple zones: o In an accident, the material in these crumple zones squashes and folds in a specific way o This crumpling and folding reduces the momentum of the car over a longer period of time (i.e reduces the rate of change of momentum) o àthe impact forces on the passengers are less o àreduced chance of serious injury WORK AND POWER ‘Work’ is done when energy is transferred from one form to another o E.g car brakes ‘do work’ by transferring kinetic energy to thermal energy The amount of ‘work’ done is equal to the amount of energy transferred Energy is measured in joules (J)àwork is also measured in joules Calculating work done: work done (joules, J) = force (newtons, N) x distance moved in the direction of the force (metres, m) o E=Fxd E.g a sailor lifts a 300 N sail from the deck to a height 4 m up. How much work does the sailor do? o Work done = 300 x 4 = 1,200 J Power: Power is the rate of doing work – measured in watts (W) Power (watt, W) = work done (joule, J) / time taken (second, s) o P=E/t o 1 watt = 1 joule of work done per second o I.e the more work done per second, the more power generated E.g a motorbike engine increases the bike’s kinetic energy over 40m, using a force of 6000 N. It takes 5 seconds to do this. What power did the engine provide? o Work done = 6000 x 40 = 240,000 J o àpower = 240,000 / 5 = 48,000 W POTENTIAL AND KINETIC ENERGY Gravitational potential energy: Gravitational potential energy is energy that is stored because of an object’s position in a gravitational field o I.e: on Earth, if something can fall (e.g a person on a diving board) it has gravitational potential energy Gravitational potential energy can be calculated using the equation…: o Gravitational potential energy (J) = mass (kg) x gravitational field strength (N/kg) x vertical height from ground (m)
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o GPE = m x g x h E.g on earth the strength of the gravitational field is 10N/kg. What is the gravitational potential energy gained by a 500kg Mars Rover when it’s lifted 15m by a test crane on Earth? o GPE = 500 x 10 x 15 = 75,000 J Kinetic energy: Kinetic energy is another name for movement energy The kinetic energy can be calculated using the equation…: o kinetic energy (J) = ½ x mass (kg) x (velocity)2 (m/s2) o KE = ½ x m x v2 E.g what is the kinetic energy of a 65kg girl running at 6m/s? o KE = ½ x 65 x (62) = 1,170 J Conservation of energy: When energy is transferred from one form to another, energy is conserved (i.e total amount always remains the same…none is lost) E.g: o As an object falls, its gravitational potential energy is converted into kinetic energy o When an object with gravitational potential energy falls down, the amount of kinetic energy it has just before it hits the ground is equal to its initial gravitational potential energy (as all the GPE has been converted to KE) E.g when a 500kg item was dropped, 75000 J of gravitational potential energy were all transferred to kinetic energy by the time it hit the ground. How fast did the item land? o KE = 75000 J (because as item falls all 75000 J of GPE is transferred to KE) o à(velocity)2 = 75000 / (½ x 500) = 300 o àvelocity = √300 = 17.3 m/s Braking distances, conservation of energy, and work done: Brakes ‘do work’ by transferring kinetic energy to thermal energy When the vehicle stops, it has no more kinetic energy (energy is conservedàall the kinetic energy has been converted to thermal energy) àthe work done to bring a vehicle to rest is equal to its initial kinetic energy… o i.e the greater the initial velocity of the vehicle, the greater its initial kinetic energy (recall: KE = ½ x m x v2)àthe more work that needs to be done to bring the vehicle to rest o This explains why the faster a vehicle is travelling, the longer its braking distance