The two blocks (m= 16 kg and M = 88 kg) are not attached to each other.The coefficient of static friction between the blocks is ms =0.38, but the surface beneath the larger block is frictionless. What is the minimum magnitude of the horizontal force required to keep the smaller block from slipping down the larger block?

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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?”