I've been working over this relatively simple problem for quite a while, and I still cannot get the answer that I'm looking for.(adsbygoogle = window.adsbygoogle || []).push({});

Here is the problem:

A car of mass M traveling at speed V approaches a hill of height H. At the bottom of the hill the engine of the car is turned off.

Show that if V > SQRT(g(1+(2H/R)) the car would come off the hill at the top of the hill. R is the radius of curvature of the road at the top of the hill.

I have worked through this quite a few times, but I cannot get that answer.

Here's what I've done.

K_i = 1/2*mv^2

U_i = 0

U_f = mgH

To find K_f, I set g equal to the radial acceleration: g = v^2/R. Then, solving for that v, I get v = SQRT(gR).

So now my K_f is K_f = 1/2*mv^2 = 1/2*mgR.

Using the conservation of energy equation, I get:

1/2*mv^2 = 1/2*mgR + mgH.

After solving for V, I get V = SQRT(g(R + 2H)) which is not equal to the answer I am looking for.

If someone could please find where I've been doing something wrong or making a bad assumption, that would be awesome. A little guidance would be very helpful right now.

Thanks a lot,

J

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# Homework Help: Conservation of Energy - not expected result

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