In the figure below, a runaway truck with failed brakes is moving downgrade at 1
ID: 1773073 • Letter: I
Question
In the figure below, a runaway truck with failed brakes is moving downgrade at 138 km/h just before the driver steers the truck travel up a frictionless emergency escape ramp with an inclination of 12°. The truck's mass is 5000 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.)
m
(b) Does the minimum length L increase, decrease, or remain the same if the truck's mass is decreased?
increasedecrease remain the same
(c) Does the minimum length L increase, decrease, or remain the same if the truck's speed is decreased?
increasedecrease remain the same
Explanation / Answer
Given
mass of truck m = 5000 kg
moving with velocity v = 138 kmph = 38.333 m/s
the angle of inclination is theta = 12 degrees
here the work done by the gravitational force causes the truck to stop after reaching to a height h
h = L sin theta
a)
now work energy theorem is
work done = change in k.e
mgL sin theta = 0.5*m*(v2^2-v1^2)
L = 0.5V^2/(g sin theta) m
L = 0.5*38.333^2/(9.8 sin12) m
L = 360.58 m
b)
the minimum length L increase, decrease, or remain the same if the truck's mass is decreased
though the truck's mass decreases there is no change in L , remains same.
c) the minimum length decreases if the speed decreased
L = v^2/2g*sin theta