The top of a small hill has a circular (vertical) cross section with an approximate radius of 57 m. A car going over this hill too fast might leave the ground and thus lose control. What speed limit should be posted?
(Hint provided: The normal force of the car as it passes this point won't be equal to the car's weight. What must it be approximately if the car's tires just barely maintain contact with the road?)
Can someone please explain to me how to go about this problem? Thanks!|||Well.... you don't want the car's wheels to leave the ground, so we'll look at the speed just when the tires lift off the hill. When the wheels lift off, this means that there is no normal force from the ground on the car. So the only to forces acting on the car (draw an FBD) are the weight of the car and the centripetal force. Do to newton's law,
W = m*a
W = weight
m = mass
a = acceleration
The weight of the vehicle is the mass times gravity.
The acceleration of the vehicle is v^/r, where v is the velocity, and r is the radius of the road.
m*g = m*v^2 /r
v = (g*r)^.5
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment