Question

A truck of mass 1.25 times 10^4 kg, initially traveling at 60mph a long a level (assumed frictionless)road, encounters a downhill grade of 6 degree, at which point the driver immediately realizes the brakes have failed. 45 seconds later, the driver steers the truck upon emergency ramp with coefficient of friction of 0.85 inclined at 10 degree above the horizontal. What minimum length must the emergency ramp have so that the truck can come to a stop?

Answer 1

The truck’s energy is initially all kinetic, and when it stops at the end of its movement up the ramp, it is all gravitational potential energy. So we can find the minimum change in height such that all the initial kinetic energy can be transformed into gravitational potential energy:

0.5*mv_i² = mgh

h = vi²/2g

vi = 60 mph = 26.8 m/s

h = 26.8^2/2*9.8 = 36.6 m

The relationship between this height and the length of the ramp is

h = l*sin(10) =======> l = h/ sin(10) = 36.6 m/ sin(10) = 210.8 m