How high a hill can a car coast up (engine disengaged) if friction is negligible

Question

How high a hill can a car coast up (engine disengaged) if friction is negligible and its initial speed is 90.0 km/h? m If, in actuality, a 750 kg car with an initial speed of 90.0 km/h is observed to coast up a hill to a height 14.0 m above its starting point, how much thermal energy was generated by friction? What is the average force of friction if the hill has a slope 2.5Degree above the horizontal? (Explicitly show on paper how you follow the steps in the Problem-Solving Strategy for energy found on pages 159 and 160. Your instructor may ask you to turn in this work.) N (down the slope)

Explanation / Answer

here,

(a)

initial speed , u = 90 km/h

u = 25 m/s

let the height reached be h

using conservation of mechanical energy

m * g * h = 0.5 * m * u^2

9.8 * h = 0.5 * 25^2

h = 31.89 m

(b)

thermal energy generated by friction , E = initial kinetic energy - final potential energy

E = 0.5 * m * v^2 - m * g * h

E = 0.5 * 750 * 25^2 - 750 * 9.8 * 14

E = 1.31 * 10^5 J

(c)

theta = 2.5 degree

distance travelled , d = h/sin(theta)

d = 23.39 m

then the average frictional force , ff = E/d

ff = 1.31 * 10^5 /23.39

ff = 5600.7 N

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