Geous for a high jumper to jump in this way . What power is required to maintain

Question

Geous for a high jumper to jump in this way . What power is required to maintain an automobile at a cruising sped of 60 mph on a level road ? Neglect all drag except that due to wind resistance . The drag forces FD on an object moving at constant speed v through a fluid is FD=1/2 pv 2 AC D Where p is the density of the fluid (air in this example), A is the frontal area of the object , and CD is its (dimensionless) drag coefficient . A good guess for the drag coefficient of an automobile is 0.25, and you can assume that it is approximately independent of speed . estimate the forntal area of automobiles by examining a few. Your result (unless you make an error ) should come somewhat as a surprise . Why is the horsepower (1 hp =746 w) rating of many automobiles so mu Ch higher than that needed for cruising even at the fairly high speed of 60 mph? Hint: calculate the average power needed to accelerate an automobile (you pick the make and model) from 0 to 60 mph in , say , 10 second. Neglect drag during the acceleration.

Explanation / Answer

a)F=0.5v2ACd

Surface area of automobile2m2

60mph=26.82m/s

=1.28kg/m3

F=0.5*1.28*26.822*2*0.25=230.2J=0.309hp

This is clearly very less than the hp rating of most automobiles.

b)a=26.82/10=2.682m/s2

Let the mass of the automobile be 1000kg

F=ma=2682N

P=Fv=2682*(26.82/2)=35962J=48.2hp

Clearly this is a very high number and justifies the hp ratings of an automobile.

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