A van of mass $3000$ kg is pulling a trailer of mass $500$ kg along a straight horizontal road at a constant speed of $25$ms−1. The system of the van and the trailer is modeled as two particles connected by a light inextensible cable. There is a constant resistance to motion of $300$ N on the van and $100$ N on the trailer.
(i) Find the power of the van’s engine.
(ii) Write down the tension in the cable.
In first part we use total resistance to get the power. Why don't we use $300$ N? How do we imagine tension in different area (string, van and trailer)?
As long as everything remains moving at constant speed, the tension in the cable must be the same everywhere along its length, and is the magnitude of the forces it exerts on the trailer and the van.
The only forces acting on the trailer are the resistance on it and the force exerted on it by the cable. Since it is moving at constant speed, these forces must balance. What does that tell you about the tension in the cable?
The only forces acting on the van are the resistance on it, the force exerted on it by the cable and the propulsive force supplied by the engine. Since the van is moving at constant speed, these forces must also balance. The reason why you don't use only the resistance, $300$ N, on the van in computing the power of the engine is because the propulsive force doesn't merely have to balance that force by itself, but the sum of that force and the force exerted on the van by the cable.