In the figure, a runaway truck with failed brakes is moving downgrade at 101 km/
ID: 1429215 • Letter: I
Question
In the figure, a runaway truck with failed brakes is moving downgrade at 101 km/h just before the driver steers the truck up a frictionless emergency escape ramp with an inclination of ? = 17°. The truck's mass is 1.1 × 104 kg. (a)What minimum length L must the ramp have if the truck is to stop (momentarily) along it? (Assume the truck is a particle, and justify that assumption.) Does the minimum length L increase, decrease, or remain the same if (b) the truck’s mass is decreased and (c) its speed is decreased?
(a) Number Units This answer has no units° (degrees)mkgsm/sm/s^2NJWN/mkg·m/s or N·sN/m^2 or Pakg/m^3gm/s^3timesExplanation / Answer
Energy conservation Theoram
KE1 + PE1 = KE2 + PE2
0.5*m*vi^2 + 0 = 0.5*m*vf^2 + mgh
h = (vi^2 - vf^2)/2g
vi = 101 km/h = 28.05 m/sec
h = 28.05^2/(2*9.81) = 40.10 m
L = h/sin A = 40.10/(sin 17 deg) = 137.15 m
B. L does not depend on m so it will remain the same.
C. as vi decrease L will also decrease because L is proportional to vi^2
Comment below if you have any doubt.
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