Suppose that a sand-filled barrier is used to stop trucks that lose their breaks

Question

Suppose that a sand-filled barrier is used to stop trucks that lose their breaks at the end of a roadway. Assuming that the barrier applies the same constant force to all of the trucks, rank the distances that the following tracks will travel from the moment they strike the barriers until they finally stop, from the smallest distance to the largest, given the mass and the initial velocity of the tracks. a) m = 1, 900 kg: v = 30 m/s b) m = 3, 900 kg: v = 5 m/s c) m = 800 kg: v = 70 m/s d) m = 3, 350 kg: v = 25 m/s e) m = 5, 350 kg: v = 50 m/s

Explanation / Answer

a) KE = (1/2)*m*v^2 = (1/2)*1900*30^2 = 855000 J

b) KE = (1/2)*m*v^2 = (1/2)*3900*5^2 = 48750 J

c) KE = (1/2)*m*v^2 = (1/2)*800*70^2 = 1960000 J

d) KE = (1/2)*m*v^2 = (1/2)*3350*25^2 = 1046875 J

e) KE = (1/2)*m*v^2 = (1/2)*5350*50^2 = 6687500 J

we know, Workdone = change in kinetic energy

F*d = delta_KE

d = delta_KE/F

so, d is proportional to delta_KE

so,

smallest -----------------------------------largest

b < a < d < c < e

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