In the figure, an airport luggage-carrying train with a tractor T is pulling three luggage carts, M₁, M₂, and M₃ with an acceleration of 1.2 m/s². If T = 300 kg, M₁ = 200 kg, M₂ = 100 kg, and M₃ = 100 kg, and air resistance is negligible, then the tension in the connection between cart M₂ and cart M₁ is A) 840 N. B) 480 N. C) 240 N. D) 120 N. E) 0 N.

Question

Quizplus · Accepted Answer

First, we can find the total mass being pulled by adding the masses of the tractor and the three carts: $M_{tot} = 300 + 200 + 100 + 100 = 700 ext{ kg}$ Next, we can find the force needed to accelerate this mass at 1.2 m/s² using Newton's second law: $F_{net} = ma = (700 ext{ kg})(1.2 ext{ m/s²}) = 840 ext{ N}$ This force is being applied to the entire train of carts, so the tension in each connection between carts must be the same. Therefore, the tension in the connection between M₂ and M₁ is also 840 N. However, the question asks for the tension specifically in the connection between M₂ and M₁. Since M₂ is in the middle of the train, it is being pulled on both sides by the connections to M₁ and M₃. The tension in the connection between M₂ and M₁ is the force required to overcome the resistance to motion of M₂ caused by the tension in the two connections. Since M₂ is being pulled with the same force on both sides and has the same mass as M₃, the tension in the connection between M₂ and M₃ must be half of the total force applied to the entire train: $F_{M₃-M₂} = \frac{1}{2}(840 ext{ N}) = 420 ext{ N}$ This means that the remaining force applied to M₂ is $F_{M₂} = 840 ext{ N} - 420 ext{ N} = 420 ext{ N}$ Therefore, the tension in the connection between M₂ and M₁ is also $420 ext{ N}$, which is closest to option C (240 N).

In the Figure, an Airport Luggage-Carrying Train with a Tractor