1. A truck with mass in has a brake failure while going down an icy mountain roa

Question

1. A truck with mass in has a brake failure while going down an icy mountain road of constant downward lope angle alpha. Initially the truck is moving downhill at speed v0. After careening downhill a distance L with negligible friction, the truck driver steers the runaway vehicle onto a runaway truck ramp of constant upward slope angle Beta. The truck ramp has a soft sand surface for which the coefficient of rolling friction in Mu r. What is the distance that the truck moves up the ramp before coming to a halt? Solve using energy methods.

Explanation / Answer

Consider here the distance moved by the truck up the ramp is =x

The speed of the truck when it is moving down the hill is=v0

The distance travelled by the truck aftercareening down the hill is =L

The upward slope angle is = ?

The kinetic energy is(k.E1)=(1/2)mv02 .

The potential energy for the truck when it moves down the rampis (P.E1) =mgLsin?

The potential energy when it moves up the rampis(P.E2) =mgxsin?

The kinetic energy is(K.E2) =0 because the finalvelocity becomes to zero.

The other work done by the rolling friction is(Wother) =-?rmgxcos?

Now from the work energy theorem

Wother = (K.E2 +P.E2)-(K.E1 +P.E1)

-?rmgxcos? = 0 + mgxsin?-((1/2)mv02 +mgLsin?)

Now from this solving for the x we that

                 x =((1/2)mv02 +mgLsin?)/mg(sin? +?rcos?)

The distance that the truck moves up the ramp before comingto stop is

                 x  =((vo2/2g)+Lsin?)/(sin?+?rcos?)

i hope this may helps you

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