A truck has wheels of diameter 0.9m, a weight of 8000kg, a wheel-base of 4m, and a tray height

Question

of approximately 1.2m. The truck’s weight distribution is 50% on the rear wheels and 50% on the front wheels. The truck’s front springs have a combined stiffness of 550,000 N/m, and the rear
springs have a combined stiffness of 600,000 N/m. The front and rear spring lengths are both 0.75m
(uncompressed). The front and rear shock absorbers (dampers) both have damping values of 30,000 Ns/m. The elastic coefficient of restitution for contact of the wheels on the road is e = 0.5.

A 3000kg package (1m by 1m) is placed on the tray of the truck with its centre of gravity 1m in
front of the rear axle. The package is not restrained and is free to slide on the tray of the truck with
friction coefficient µs=µk=0.5. The truck then travels over a triangular speed bump 100mm high and 300mm wide.

(a) Determine the maximum velocity at which the truck can cross the speed bump without the package moving relative to the tray.

(b) Determine the maximum acceleration which the package experiences when crossing the
bump at this speed.