Consider the figure on the left, in which two blocks are being pushed across a frictionless surface. The blocks have masses m1 = 3kg and m2 = 15kg. (a) How hard are you pushing on m1, if the acceleration of m2 is 6m/s2? (You are pushing horizontally, as shown in the figure.) (b) What is the contact force between m1 and m2? (Still focusing on the figure on the left.) (c) Now consider the figure on the right, in which m2 is lifted off the ground. If the coefficient of static friction between m1 and m2 is 0.2 how hard would you have to push the blocks to ensure m2 would not slide down m1?

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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?”