Final answer:
This Physics problem is about calculating the maximum acceleration a two-wheel drive utility truck can achieve and determining if a metal cabinet on it will slip when accelerating at that rate, then adjusting the calculation for a four-wheel drive scenario.
Step-by-step explanation:
The subject of this question is Physics, focusing on the concepts of force, mass, acceleration, and friction. We are dealing with a 1.00 × 10³ kg utility truck and its ability to accelerate on dry concrete. The two parts of the problem involve calculating the maximum acceleration of the truck with its weight supported by different numbers of drive wheels and analyzing whether a metal cabinet would slip from the truck bed under this acceleration.
Part a (Two-wheel drive)
With half of the weight on the two drive wheels, this means each wheel supports 500 kg. If the coefficient of static friction μs (typical for dry concrete and rubber) is around 1.0, the maximum static frictional force (friction before sliding begins) is equal to the normal force (the weight supported by the drive wheels) times the coefficient of static friction. Therefore, the maximum frictional force Ff is Ff = mgμs, where m is the mass supported by the wheels (500 kg) and g is the acceleration due to gravity (9.8 m/s²). The maximum acceleration amax of the truck is then found using Newton's second law, Ff = ma.
Part b (Slip condition)
To determine if the cabinet will slip, we compare the force required to accelerate the cabinet (which is a product of the cabinet's mass and the truck's acceleration) with the maximum static frictional force between the cabinet and the bed of the truck. If the required force is greater than the static frictional force, the cabinet would slip.
Part c (Four-wheel drive)
If the truck has four-wheel drive, all the wheels contribute to the frictional force. The overall mass used to calculate the frictional force is now the full mass of the truck. Consequently, both the potential maximum acceleration and the condition for slipping change with the different drive configurations.