Final answer:
The question pertains to finding the final velocity of a baggage tractor system after 3 seconds using a given time-dependent force, and the force in the connecting cable between the tractor and a cart. This involves calculating total impulse and using it to determine the system's final velocity, then applying Newton's second law for the cable force.
Step-by-step explanation:
To solve part (a) of the question about the baggage tractor, we need to calculate the speed after 3.00 seconds using the given driving force formula F = (820.0t) N. Since the driving force varies with time, we first determine the impulse delivered to the tractor and carts system over the 3 seconds and use this to find the final velocity.
- Calculate the total impulse delivered to the system by integrating the force over the time interval:
I = \( \int_{0}^{3} 820.0t \, dt \)
This integral yields I = \( \frac{1}{2} \times 820.0 \times 3^{2} \) N\(\cdot\)s. - Impulse is also equal to the change in momentum of the system, I = \( \Delta p = m \times \Delta v \), where m is the total mass of the tractor and carts and \( \Delta v \) is the change in velocity from rest.
As the system starts from rest, \( \Delta v \) is just the final velocity after 3 seconds. - The total mass of the system m is 650.0 kg + 250.0 kg + 150.0 kg = 1050.0 kg.
- Now solve for \( \Delta v \):\( \Delta v = \frac{I}{m} \).
- Finally, we can use the calculated impulse and total mass to determine the final velocity.
For part (b), to find the horizontal force acting on the connecting cable between the tractor and cart A at this instant, we need to consider Newton's second law. With the acceleration known from part (a), we can determine the force by taking the acceleration of cart A and multiplying it by its mass.