Final answer:
Trucks with dump bodies are required to have positive means of support. The magnitude of maximum acceleration for a utility truck half-supported by two drive wheels on dry concrete is about 4.9 m/s², and a metal cabinet might slip if it's not properly secured or if its static friction with the wooden bed is too low. With four-wheel drive, the truck's maximum acceleration is potentially doubled to about 9.8 m/s².
Step-by-step explanation:
Trucks with a dump bodies must be equipped with positive means of support, permanently attached, and capable of being locked in position to prevent accidental lowering of the body during maintenance or inspection. The correct answer is 1) Positive.
To answer the physics problem about a 1.00 × 10³ kg utility truck, we need to assume typical values for coefficients of friction since they are not provided. The static friction coefficient between dry concrete and rubber tires can be around 1.0. Knowing this and that half of the truck's weight is supported by its two drive wheels, the available traction force for acceleration is approximately equal to the static friction force, which would be the weight on the two drive wheels times the coefficient of friction.
With a truck mass of 1.00 × 10³ kg, the gravitational force (weight) would be 1.00 × 10³ kg × 9.8 m/s². Considering that half of this is supported by the drive wheels, we get a traction force of about 4.9 kN. The maximum acceleration, a, can be found using Newton's second law, F = ma, leading to a = F/m, which in this case would be around 4.9 m/s².
As for the metal cabinet on the wooden bed of the truck, it will slip if the static friction force between the cabinet and the wood (which depends on the cabinet's weight and the coefficient of static friction between metal and wood) is less than the force required to accelerate the cabinet at the same rate as the truck. If the coefficient of static friction between the metal cabinet and the wooden bed is less than 0.49, the cabinet will slip when the truck accelerates at its maximum rate.
If the truck had four-wheel drive, the entire weight of the truck would contribute to the static friction force. This would double the total available traction force, and consequently, the maximum achievable acceleration on dry concrete would be about 9.8 m/s², assuming the same coefficient of friction. The metal cabinet would be even more likely to slip unless it is secured, due to the higher acceleration of the truck.