Constant Horizontal Force and Rolling Friction: A Reflective Analysis

When the coupling of the trailer at point A fails, the trailer has a mass of 250 kg and is coasting at a speed of 20 km/h. As a result, the trailer coasts a distance of 85 m before coming to a complete stop.

To determine the constant horizontal force F created by rolling friction that stops the trailer, we need to apply the work-energy principle. This principle states that the work done by a force is equal to the change in kinetic energy of the object it acts upon.

The work done by the force of rolling friction in stopping the trailer is equal to the initial kinetic energy of the trailer. The initial kinetic energy of the trailer can be calculated using the formula:

Initial Kinetic Energy = 0.5 * mass * velocity^2

Plugging in the values, we get:

Initial Kinetic Energy = 0.5 * 250 * (20 km/h)^2

Initial Kinetic Energy = 0.5 * 250 * (20 * 1000/3600)^2 (converting km/h to m/s)

Initial Kinetic Energy = 0.5 * 250 * (5.56)^2

Initial Kinetic Energy = 0.5 * 250 * 30.95

Initial Kinetic Energy = 3878.125 Joules

Since the trailer comes to a complete stop, the work done by the force of rolling friction is equal to the initial kinetic energy of the trailer. Therefore:

Work done by rolling friction = Force * Distance

Work done by rolling friction = F * 85 m

Setting the work done by rolling friction equal to the initial kinetic energy and solving for F:

F * 85 = 3878.125

F = 3878.125 / 85

F = 45.56 N

Therefore, the constant horizontal force F created by rolling friction that causes the trailer to stop is approximately 45.56 Newtons.