00:01
Let us begin with subpart a.
00:04
Here we have mass of truck as 22 ,000 kilograms.
00:11
The truck heads down a slop at an angle, theta 1 equals 3 .5 degree and it moves with a velocity of 20 meter per second.
00:24
The runaway ramp slopes at an ankle theta 2 equals 10 degrees and the runaway ramp is at a distance x equals to 600 meter ahead of the truck.
00:39
The coefficient of rolling friction, mu r is given as 0 .4.
00:44
Now let d be the distance, distance along the ramp.
00:51
Distance along the ramp when the truck stops.
00:57
So these are the given information.
01:00
Now we need to calculate the distance along the ramp stop that is we have to determine d now from conservation of energy the initial energy that is on pavement this will be equals to the final energy that is on ramp so this is on pavement and the final energy you're considering it this is on ramp so we have the initial energy as kinetic energy initial kinetic energy plus initial potential energy equals final kinetic energy plus final potential energy plus the work done by the friction so here the truck stops after some time so the kinetic energy or the final kinetic energy will be zero so we have kinetic energy initial plus the potential initial potential energy equals the final potential energy plus the work done by the friction.
02:06
Now we can write expressions for each of these terms.
02:11
So we have initial kinetic energy as half mv square plus.
02:15
Initial potential energy is mg x sine theta 1.
02:21
And this is equals to final potential energy will be mg d sine theta 2.
02:27
And work done by friction will be f into d.
02:31
Or frictional force into displacement.
02:36
Now we know that frictional force, sorry, frictional force f, this will be equals to mu r mg, that is coefficient of rolling friction into normal force.
02:48
So mu r into mg cos theta.
02:52
Now we can substitute this in the above expression.
02:55
So we get half mv square plus mg x sine theta 1.
03:04
Equals mg d sine theta 2, mgd sine theta 2 which is the final potential energy plus mu rmg cos theta into d which is the work done by the friction.
03:28
Now here we can cancel all the m now we get v square by 2 plus g x sine theta 1 equals we can take g and d as common terms so we get g into d into sine theta 2, sine theta 2 plus new r into cos theta 2, cos theta 2...