Final answer:
The maximum acceleration of a utility truck with weight supported on two drive wheels can be calculated using the coefficient of friction for rubber on dry concrete and the truck's mass. Determining if a metal cabinet will slip depends on comparing the truck's acceleration with the static friction coefficient. With four-wheel drive, these calculations are adjusted to reflect the greater normal force.
Step-by-step explanation:
To answer part (a), we need to calculate the maximum acceleration of a 1.00 × 10³ kg utility truck when half of its weight is supported by its two drive wheels. The force of friction, which provides the acceleration, depends on the coefficient of friction (μ) and the normal force (N). On dry concrete, μ is typically around 0.7 for rubber tires. The normal force here is half the truck's weight, so N = (0.5 × 1.00 × 10³ kg × 9.8 m/s²). The maximum force of friction is μ × N which can then be set equal to the mass of the truck times its maximum acceleration (ma), from which we solve for a (acceleration).
For part (b), we determine whether the metal cabinet will slip by comparing the truck's acceleration to the static coefficient of friction between the cabinet and the wooden bed. If the truck's acceleration exceeds the product of the static friction coefficient and gravity, the cabinet will slip.
In part (c), when assuming the truck is four-wheel drive, the same principles apply, but the normal force is now distributed over four wheels instead of two, allowing potentially greater maximum acceleration and a different analysis of the cabinet's tendency to slip, taking into account the increased normal force.