posted by Anonymous .
(a) How high a hill can a car coast up (engine disengaged) if work done by friction is negligible
and its initial speed is 110 km/h? (b) If, in actuality, a 750-kg car with an initial speed of 110 km/h
is observed to coast up a hill to a height 22.0 m above its starting point, how much thermal energy
was generated by friction? (c) What is the average force of friction if the hill has a slope 2.5°
above the horizontal?
110 km/hr = 110,000 m/3600 s = 30.6 m/s
m g h = (1/2) m v^2
9.81 h = .5 (30.6)^2
h = 47.7 meters
(b) loss of energy = m g (47.7-22)
= 750(9.81)(25.7) = 189,000 Joules lost
(c) work done = force in direction of motion * distance moved
189,000 = F (22/sin2.5)
F = 375 N
You are welcome.
I disagree with the answer to (c). The distance traveled (d) is not the same as the height the car has reached at the end of its coasting. d is actually the hypotenuse. so h=dsin(2.5) thus d=h/sin(2.5), so d=22/0.424 which is 52.1, the distance traveled. Plugging this into the work done by friction,(Wf), Wf= Fdcos(2.5), F= Wf / dcos(2.5),F = 189,000/52.06cos2.5 = 3634N.