What is the angle for an expressway off-ramp curve of radius 50.0 m at a design speed of 50.0 km/h (14.0 m/s)?

Question

anonymous · Answer

@JFraser :)

jfraser · Answer

you need some trig for this one, hang on.

anonymous · Answer

sure thankyou :)

jfraser · Answer

because the car is traveling in a circle, it will experience a centripetal force towards the center, keeping it on the road. because it's traveling on an angle, it can travel at a greater speed than if it were on a flat road. The maximum speed of a car along a banked curve depends on the radius of the curve (which you know) and the angle of the road (which you don't).

The picture has different numbers, but the idea is exactly the same. Find the force needed to keep the car on the road, and set that equal to m*ac. You have to work backwards and find the angle of the track using the speed and total force.

jfraser · Answer

attachment

anonymous · Answer

oh okay :)

jfraser · Answer

you know the speed of the car, and you know the radius of the road. Find ac$$a_c = \frac{v^2}{r}$$that acceleration is also part of newton's second law$$F_c = m*a_c$$you know the acceleration and the mass, find the centripetal force.

jfraser · Answer

because of the angle, the centripetal force is also equal to the normal force times the sine of the angle$$F_c = F_n * \sin \theta$$you know the Fc, you can find Fn, do the inverse sine to find the angle

anonymous · Answer

uhm, how do you find Fn again? :)

jfraser · Answer

Fn is the normal force, which is the weight of the car (m*g)