ball of mass m=0.49 kg hangs on a light rope from the ceiling of a train. The train accelerates forward, on horizontal tracks, in the positive x direction. The string makes an angle of ϕ=31∘ with vertical. A coordinate system is provided.  Part (b)  Write an expression for the vertical component of the net force.  Part (c)  What is the numeric value, in newtons, of the tension in the rope?   Part (d)  What is the magnitude, in meters per squared second, of the acceleration of the train?

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Newton’s Third Law of Motion

The horse pulls the cart and the cart pulls the horse in response as per Newton third law. So the big question is, “Don’t the two forces cancel each other? How does the cart accelerate?”