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When the box is placed on the tailgate of the truck, it creates torque around the rear axle. But what exactly is torque? Torque is a measure of the tendency of a force to rotate an object about an axis. In simpler terms, torque is what causes an object to spin or turn.
The formula for torque \(\tau\) is given by: \(\tau = F \times d\), where \(F\) is the force applied, and \(d\) is the distance from the axis of rotation to where the force is applied, known as the lever arm.
In this problem, the box adds a force of 3600 N at a distance (lever arm) of 1.00 m behind the rear axle. This torque affects how the weight is distributed between the front and rear wheels. The placement of the box shifts the vehicle's balance, demonstrating the power of torque to change how loads are supported.

Weight distribution is crucial in determining how the truck remains balanced. Initially, the truck's weight is divided between the front and rear wheels with 10,780 N resting on the front wheels and 8820 N on the rear.
When the box is placed on the tailgate, it not only adds weight to the truck but also changes the distribution of that weight. This shift occurs because the added mass at the rear increases the torque around the rear axle. The result is a redistribution of weight, decreasing the load on the front wheels.
If more weight is needed on the rear to lift the front wheels off the ground, we should add enough mass to counteract the torque created by the entire weight previously on the front wheels. This way, the balance is tipped entirely to the back, illustrating how placement of weight affects stability.

The behavior of the truck and the effect of placing a weight on the tailgate can be understood clearly through Newton's Laws of Motion. Newton's First Law states that an object will remain at rest or in uniform motion unless acted upon by a net external force. In the truck's case, it stays static until forces (like the added weight and resulting torque) act upon it.
Newton's Second Law explains how the acceleration (or in this case, the shift in load) occurs when the mass of the box changes the equilibrium of forces acting on the truck. The mass, combined with gravity, introduces a force that shifts the weight distribution.
Finally, Newton's Third Law says that for every action, there is an equal and opposite reaction. Perhaps less obvious in this context, but significant nonetheless: the road exerts an upward force on the truck, counteracting the forces due to the truck's weight, and this interplay keeps the truck in balance. Understanding these laws helps in analyzing how weight placement and resultant forces affect movement and balance.