It is a cold, icy miserable day in Whitehorse. You find yourself driving along the highway on your way out of town. You are driving a little fast (80km/h) as you approach a very icy corner on the highway, the corner essentially is frictionless. Luckily the engineers realised tourists like you would drive too fast into this corner and designed the corner to be banked and allow cars to safely navigate the 80m radius turn. At what angle did the engineers bank the corner?
5 years ago
Answered By Joel C
The car is driving on a banked, frictionless curve so there will be two forces: Normal force and the force of gravity on the car. Fnet is equivalent to the x-component of the normal force and also the centripetal force. Therefore mv2/r (centripetal force) = mgtan $\theta$θ (x-component of the normal force). You can take the mass away from both sides and rearrange the equation to determine the angle, in which tan-1 (v2/rg) = $\theta$θ . Place the numbers provided in the question into the equation and the final answer comes out to be 83 degrees (make sure graphing calulators are placed in degree mode rather than radian mode). Therefore, the engineers bank the corner at 83 degrees to allow cars moving at 80km/h to safely navigate the 80m radius turn.
5 years ago
Answered By Clifton P
While I completely agree with the answer above I have to ask if perhaps the question had a typo. With a radius of 80m and an angle of 83 degrees, your car is almost completely sideways during the turn(ie you would look out your side window and see the ground). However if the radius were say, 800m, you get an angle of 39 degrees which is closer to real world roads, unless you’re on a racetrack.