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,then the force 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, let's find the total mass of the system: Total Mass = T + M₁ + M₂ + M₃ Total Mass = 300 kg + 200 kg + 100 kg + 100 kg Total Mass = 700 kg Now we can find the total force required to accelerate the system: F = ma F = 700 kg * 1.2 m/s^2 F = 840 N This is the total force applied by the tractor T to the entire system. In order to find the force in the connection between cart M₂ and cart M₁, we need to subtract the forces applied by the other carts in front of it. Since the carts are connected, the force applied by each cart is the same as the force applied to it. The force applied by cart M₃ is: F13 = ma F13 = 100 kg * 1.2 m/s^2 F13 = 120 N This is the force applied by cart M₃ to cart M₂. Now we can find the force applied by cart M₂ to cart M₁: F12 = ma F12 = 100 kg * 1.2 m/s^2 F12 = 120 N Therefore, the total force in the connection between cart M₂ and cart M₁ is: F11-12 = 840 N - 120 N - 120 N F11-12 = 600 N But we need to divide this by 2, because the force is being applied by two connections between the carts: F11-12 = 600 N / 2 F11-12 = 300 N Therefore, the force in the connection between cart M₂ and cart M₁ is 300 N, which is answer choice C.

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