If action = reaction, how does anything move?

SDStaff Karen Lingel replies:

I’m not sure the Straight Dope is the ideal place to deal with basic physics, but if the schools have failed our young people, I guess it’s up to us.

Your question brings to mind the canonical physics exam question: A cup sits on a saucer on a table on the earth. The earth’s gravity pulls down on the cup. What is the equal-and-opposite force required by Newton’s second law? Half the students will say the saucer pushing up on the cup. WRONG! It’s the cup’s gravity pulling up on the earth!

The key to dealing with equal-and-opposite forces is to remember that they’re acting on different objects — that’s why the forces don’t cancel out. To help students isolate the forces acting on an object, physics teachers tell them to mentally draw a plastic bag around it. Say you’re pushing a box across the floor. Yeah, the box is pushing you back, but that’s irrelevant — all we’re concerned about is the forces acting on the box. So draw a plastic bag around it. The forces acting on the box include you pushing it, gravity pulling it down, the floor pushing it up, and the friction of the floor preventing it from sliding freely. Whether the box moves at all depends on the sum of the forces acting on it alone.

Now let’s isolate you. You have the force of the box pushing back on you, the gravity of the earth pulling you down, the floor pushing you up, and the friction of the floor giving you traction so you can push forward. The force that allows you to move forward is the friction from the floor! (You wouldn’t move forward if the floor were made of slippery ice.) The equal-and-opposite force isn’t some mysterious additional thing also acting on you, it’s your feet pushing against the floor. That force isn’t your problem; the floor has to deal with it.

Let’s isolate the floor. It has the force of your weight pushing it down, gravity pulling it down, beams and joists holding it up, your feet trying to push the floor horizontally backwards as you get traction, and walls or nails or friction against the joists keeping the floor from sliding horizontally out of your house. Why doesn’t the floor move? People forget — a force can cause an acceleration or a deformation. The floor doesn’t accelerate, but it bows a bit.

Let’s isolate the house. OK, let’s not — no need to make this as long as one of Dex’s religious columns. The point is clear enough: Equal-and-opposite forces aren’t a recipe for paralysis. If you’re looking for an excuse not to move boxes, you’ll have to blame your bad back.

SDStaff Karen Lingel, Straight Dope Science Advisory Board

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