Final answer:
Using Newton's second law, we find the acceleration by integrating the time-varying force and then calculate the system's speed after 3 seconds. The force on the connecting cable is determined by considering the masses involved and applying the same principles of dynamics.
Step-by-step explanation:
Finding Speed and Horizontal Force in a Baggage Tractor System
To solve for the speed of the baggage tractor system after 3.00 seconds, we need to use Newton's second law of motion and the formula for acceleration. Newton’s second law states that force equals mass times acceleration (F = ma). The total mass of the system is the sum of the masses of the tractor, cart A, and cart B.
Total mass = 650.0 kg + 250.0 kg + 150.0 kg = 1050.0 kg.
The driving force varies with time and is given by F = (820.0t) N. Throughout 3.00 s, this equation gives us the force applied at each moment. To find the acceleration, we need to integrate the force concerning time over the 3 seconds and then divide it by the total mass.
Acceleration is given by dividing the change in momentum by the time interval and total mass.
To calculate the final speed (V) after 3.00 seconds, we integrate the acceleration equation from 0 to 3 seconds.
The horizontal force on the connecting cable between the tractor and cart A at 3.00 seconds can be calculated using the same approach, considering only the masses of the tractor and cart A, as cart B will not affect the cable force between the tractor and cart A.