Final answer:
The magnitude of the average net force on the car in the sandy section of the road is calculated using the work-energy principle. The net force is determined to be 2660 N, acting opposite to the car's movement.
Step-by-step explanation:
The student is asking about calculating the magnitude of the average net force on a car that slows down as it passes through a sandy stretch. The problem can be solved using the work-energy principle, which equates the work done by the net force to the change in kinetic energy of the car. The change in kinetic energy (ΔKE) is given by the difference in kinetic energy before and after traversing the sandy stretch, which is ΔKE = 0.5 × m × (v_f^2 - v_i^2).
We have the initial velocity (v_i = 19 m/s), final velocity (v_f = 13 m/s), mass of the car (m = 1400 kg), and the distance (x = 25.0 m) traveled through the sand. The net force (‘F’) acting against the car is found by equating the work done (W = F × x) to the change in kinetic energy. Therefore, F = ΔKE / x.
First, we calculate ΔKE: ΔKE = 0.5 × 1400 kg × ((13 m/s)^2 - (19 m/s)^2) = -66500 J (negative because kinetic energy is decreasing). Now, we find the average net force: F = -66500 J / 25.0 m = -2660 N. The negative sign indicates that the force is acting in the opposite direction to the movement of the car.