2 when it is burned 1 gallon of gasoline produces 13108j of...

When it is burned, 1 gallon of gasoline produces 1.3×10^8 J of energy. A 1500 kg car accelerates from rest to 36 m/s in 10 s. The engine of this car is only 15% efficient (which is typical), meaning that only 15% of the energy from the combustion of the gasoline is used to accelerate the car. The rest goes into things like the internal kinetic energy of the engine parts as well as heating of the exhaust air and engine. a) How many gallons of gasoline does this car use during the acceleration? Express your answer using two significant figures. b) How many such accelerations will it take to burn up 1 gallon of gas? Express your answer using two significant figures.

Transcript

00:02 Here first we will assume that the car is moving on a horizontal road and a level of horizontal road is taken as y equal to zero by using conservation of energy we can write initial kinetic energy plus initial potential energy plus work done by forces other than gravity is equal to final kinetic energy plus final potential energy as the car starts from rest so initial kinetic energy is zero plus initial potential energy of car is also equal to zero plus work done by forces other than gravity here work is done by engine that is equal to final kinetic energy which is half times mass of car is 1500 kilograms into final speed of car is 37 meter per second plus funnel potential energy of car is as equal to zero this gives us work done by engine equal to 10267 jules so this is the amount of work done by engine so this is output work of engine as it is given that efficiency of the engine is only 15 % so the engine converts only 15 % of the energy obtained from burning of gasoline into useful work.

02:43 Now we can calculate energy used by engine per gallon to accelerate the car that is equal to 15 % of 1 .3 times 10 to the power at as this is the energy which is obtained when one gallon of gasoline burned so we have useful energy obtained by engine for one gallon equal to 1 .95 times 10 to 7 june now we can easily calculate number of gallons of gasoline used by engine to accelerate the car from zero meter per second to 37 meter per second so we use here ratio method so here we have number of gallons and here we have the energy that is used by engine so far 1 gallon the energy that is the useful energy that is energy used by engine is 1 .95 times 10 to the power 7 jule so this is the output energy of heat engine and here amount of energy needed to accelerate the car is 1 .26 750 jule so this is the amount of work done by engine to accelerate the car so this is the useful energy needed for engine and if we want here the number of gallants required to achieve this energy so here number of gallons and energy and energy used by engine are directly proportional so we we can write x upon x ratio 1 is equal to 1026 750 jule ratio 1 .95 times 10 to 7 jule so this gives us x equal to 0 .053 gallons so the engine needs 0 .053 gallons so the engine needs 0 .0 0 .53 gallons of gasoline in order to accelerate the car from 0 to 37 meter per second in 10 seconds...

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