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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.
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
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