Conservation of energy of speeding truck

1. Oct 31, 2004

tre2k3

I tried many ways to perfomr this problem, but i just cant figure out whether or not Im using the right values.

"A 25 ton truck loses it brakes and reaches the bottom of a hill with a speed of 60 mph.
Fortunately, there is a runaway truck ramp which is inclined at angle of 15 degrees to the horizontal."
Assuming no losses, what distance does the truck travel along the runaway truck ramp? (miles) ?

The KE of the truck just before it goes up the ramp is 6010000 ft-lb.

What do I need to do to get the distance the truck travel along the ramp? The length of the ramp is 1 mile if that means anything.

Heres a formula Ive used : KE1+PE1+Work=KE2+PE2+Eloss

Last edited: Oct 31, 2004
2. Oct 31, 2004

Staff: Mentor

Since there are no losses, mechanical energy is conserved. Measure PE from the bottom of the ramp, then the intial KE will be completely transformed to PE. Find the height the truck must rise, then figure out how far it must have traveled up the ramp to gain that height. Pay attention to units!

3. Oct 31, 2004

tre2k3

yeah, I think the units will get me. I had to convert from ton and mph to kg and m/s and divide that by 1.36 J just to get ft-lb.

4. Oct 31, 2004

tre2k3

Since I kind of new to this concept, how exactly do I go about measuring the bottom of the ramp. Do I set the value of h to 0 in mgh. Does the lenght of the ramp matter at all?

5. Oct 31, 2004

Staff: Mentor

Yes, at the bottom of the ramp set h = 0.

Think this way: Set $1/2 m v^2 = mgh$. Once you find h, relate h to the distance up the ramp (d): $d sin\theta = h$.

6. Oct 31, 2004

tre2k3

nevermind about the lenght of the ramp, that was justg the distance til the truck gets to the ramp.

7. Oct 31, 2004

tre2k3

i got it :rofl:

8. Oct 31, 2004

tre2k3

One more thing. I having trouble understandin this one.
"If instead of there being no losses, there is gravel on the runaway truck ramp that provides a constant force of 2620 pounds in the opposite direction of motion. What distance does the truck travel along the runaway truck ramp in this case?" (miles)

Do I calculate the energy loss? And do I use cos180 in the equation also?

9. Nov 1, 2004

Staff: Mentor

Yes, you must calculate the work done by that resistive force. Mechanical energy is no longer conserved: the change in energy will equal the work done by that resistive force. You'll find that the truck will stop in a shorter distance up the ramp.
Yes, since the work done by that force is negative.

10. Nov 1, 2004

tre2k3

since i dont know the height in the equation, how do I relate that to the poisition

11. Nov 1, 2004

Staff: Mentor

The same as before: see post #5. You can write your energy equation using only d (distance up the ramp) and not h. Then you'll solve for d, of course.