Question

Disturbed by speeding cars outside his workplace, Nobel laureate Arthur Holly Compton designed a speed bump (called the "Holly hump") and had it installed. Suppose a 1 800-kg car passes over a hump in a roadway that follows the arc of a circle of radius 18.8 m.
a. If the car travels at 33.0 km/h what force does the road exert on the car as the car passes the highest point of the hump?
b. What is the maximum speed the car can have without losing contact with the road as it passes this highest point?

// I have done this problem so many different ways, I must be missing something obvious

Answer 1

I think the question is a little unfair, since presumably the front and rear wheels pass over the hump separately - are we to assume that the weight of the car is evenly distributed between the front and rear points of contact ?

Also, I am going to assume that the question is asking for the vertical force exerted by the road as the point of contact passes over the highest point of the bump.

The way to solve the problem is to equate the net vertical force on the car to its acceleration towards the centre of the hump's circle of curvature as it passes over the top of the hump.

Answer 2

In other words, if m is the mass carried on each axle (900 kg ?) and N is the reaction force of the road, we require\[mg-N=\frac{ mv^2 }{ r }\]
this can be rearranged to find N for your assumed value of m etc.

For part (b), the car will be just about to leave the road when the normal reaction is zero. This condition allows you to find the corresponding value of v, which happily is independent of m.

Answer 3

Take care with the units for speed - km/h need to be converted to m/s.

Answer 4

I have numbers if you want to check your answers.

Answer 5

Thank you! I got the answers correct and I greatly appreciate your help!

Answer 6

glad i could help