Final answer:
To find the maximum acceleration of a truck, use the normal force on the drive wheels and the coefficient of static friction for dry concrete. Newton's second law allows calculation of acceleration. For a metal cabinet not to slip, the truck's acceleration must not exceed the static friction between cabinet and wood.
Step-by-step explanation:
To determine the maximum acceleration a utility truck can achieve on dry concrete, we need to consider the coefficient of static friction and the force of friction. Given that the truck's weight is evenly distributed, half of the truck's weight, which is 1.00 × 10³ kg, is supported by the drive wheels. Therefore, the force due to gravity (weight) acting on the drive wheels is 500 × 9.8 N. The frictional force, which equals the maximum force before slippage, is the product of the normal force and the coefficient of static friction (μm). Assuming μm for dry concrete is around 0.6 to 0.85, you would multiply the normal force by this range to find the frictional force.
The maximum acceleration (“a”) can be found using Newton's second law, F = ma, where F is the frictional force, and the mass “m” is 500 kg (half the truck's mass). Calculating this gives you the maximum acceleration.
Regarding whether a metal cabinet lying on the wooden bed of the truck will slip, this depends on the coefficient of static friction between the cabinet and the wood. If the truck's acceleration exceeds the maximum static frictional force between the cabinet and the truck's bed, the cabinet will slip. For four-wheel drive, the calculations would be adjusted to consider the force distributed across all four wheels, which would change the maximum acceleration and potential for the cabinet to slip based on the new distribution of forces.