Question

a. How high a hill can a car coast up (engine disengaged) if friction is negligible and it’s initial speed is 92.0km/hr? In m

b. If, in actuality , a 750 kg car with an initial speed of 92.0 km/hr is observed to coast up a hill to a height of 17.0 m above it’s starting point, how much thermal energy was generated by friction? In Joules

C. What is the average force of friction if the hill has a slope of 2.5 degrees above the horizontal ? _____ N (down the slope )

Answer 1

(a) Covert the speed in m/s.

92.0 km/h = (92 x 1000) / (60 x 60) = 25.6 m/s

Suppose the height upto which the car coast up is 'h' meter.

Use the expression for conservation of energy -

m*g*h = (1/2)*m*v^2

=> h = v^2 / (2*g) = 25.6^2 / (2*9.8) = 33.3 meter (Answer)

(b) Total initial energy of the car, Ei = Kinetic energy of the car

= (1/2)*m*v^2 = 0.5*750*25.6^2 = 245760 J

Final energy of the car, Ef = Potential energy of the car

= m*g*h = 750*9.8*17 = 124950 J

Therefore, thermal energy generated by friction = Energy loss of the car

= Ei - Ef = 245760 - 124950 = 120810.0 J

(c) Now length of the slope = L = h / sin2.5 = 17.0 / sin2.5 = 390 meter

Suppose frictional force = Ff

So, we have -

Ff x 390 = 120810

=> Ff = 120810/390 = 310.0 N (Answer)