Suppose a car approaches a hill and has an initial speed of 110 km/h at the bott

Question

Suppose a car approaches a hill and has an initial speed of 110 km/h at the bottom of the hill. The driver takes her foot off of the gas pedal and allows the car to coast up the hill. (a) If the car has the initial speed stated at a height of h - 0 how high, in meters, can the car cost up a hill if work done by friction is negligible? (b) If, in actuality, a 790- kg car with an initial speed of 110 km/h is observed to coast up a hill and stops at a height 2.2 m above its starting point, how much thermal energy was generated by friction is J?

Explanation / Answer

Given

car coasts up a hill with velocity v = 110 kmph = 110*5/18 m/s ,

so that there is no friction then the car can reahc a height h

by using conservation of energy k.e = p.e

       0.5*mv^2 = mgh

       h = v^2/2g = (110*5/18)^2 /(2*9.8) m = 47.635 m

if mass of car is m = 790 kg, and coasts the hill and stops at 22m , due to friction the energy lost is in the form of thermal energy

       the height difference is 47.635 -22 m = 25.635 m

the energy lost is w = mgh = 790*9.8*25.635 J

           = 198466.170 J

thermal energy is = 198466.170 J

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