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Equal and Opposite

July 5th, 2008 · 4 Comments

A few days ago I wrote about how to move in space, you needed to bring along something to push against. Dr. Pion objected. “It’s not what you push against that makes you move, it’s what pushes against you.”, if I can paraphrase.

I thought that was a silly objection. It’s true, but doesn’t everyone know that something you push against necessarily pushes back with the same force? It’s Newton’s Third Law, and equivalent to conservation of momentum besides.

But thinking about it some more and remembering teaching intro mechanics, no it’s not necessarily so obvious to a lot of people starting out in physics. And physicists ought to be precise with their language to avoid conceptual mistakes. Consider the following scenario: you have a truck pulling a trailer. No matter how hard the truck pulls on the trailer, the trailer pulls equally hard back on the truck due to Newton’s Third Law. How is it that the truck ever gets anywhere? This is a suprisingly confusing question to many students in their first mechanics class.

Look at the truck. There’s two forces acting on it. The road is pushing the truck tires and the trailer is pulling backwards on the truck. The first force is larger and thus the truck accelerates forward. Same thing for the trailer; there’s one force acting on it - the truck pulling it forward, and so the trailer accelerates forward as well. To actually calculate the forces requires knowing the masses of each vehicle, but if you know those the calculation is very simple because of the constraint that both vehicles have to have the same acceleration to remain connected.

In summary, when thinking about “equal and opposite reactions” it doesn’t matter in the slightest what you’re pushing on. What matters is what’s pushing on you. The fact that those forces happen to be the same is important but not the whole story.

Tags: Physical Concepts

4 responses so far ↓

  • 1 Uncle Al // Jul 5, 2008 at 2:11 pm

    A car doing 60 mph smashes head on into a solid wall. A car doing 60 mph smashes head on into an identical car doing 60 mph in the opposite direction. In particle physics it makes a big difference. How ’bout on the 6 o’clock news?

    Matt replies: No, it makes pretty much no difference in particle physics because there isn’t anything really analogous to hitting a solid wall. An experiment like the LHC collides particles head on, like the cars. An experiment like SLAC which shoots particles at a stationary target would be more like a car smashing into another parked car. Modulo relativistic effects, the analogy holds pretty tightly. There’s just no solid walls at the sub-nuclear scale.

  • 2 CCPhysicist // Jul 6, 2008 at 11:52 am

    A VW has a collision with an Escalade. Which experiences the greater force?

    Matt replies: They both experience the same force. Conservation of momentum requires that the Δp each vehicle undergoes must be equal and opposite. Since each experiences the collision for the same amount of time, equal and opposite impulses imply equal and opposite forces.

  • 3 CCPhysicist // Jul 7, 2008 at 2:12 pm

    That’s not a particularly good answer. You should just say it is because of the Third Law. If you invoke conservation laws, you should start with Noether’s theorem. ;-)

    Now that I have seen WALL-E, I remain concerned with your earlier article about movement in space with the fire extinguisher. The physics of that part of the story was handled perfectly.

    Bogosity raised its ugly head with the reference to micro gravity (objects on the ship were not weightless) and when the electromagnet turned itself on without any external source of power, as well as a few other glaring bits of nonsense (like disposing of vast quantities of trash for 700 years without running out of anything).

    I thought the film was below average for Pixar, saved only by all of the inside jokes. Favorite: based on the boot-up sound, WALL-E is a Mac.

    PS -
    Ask your fellow students that question, or get one of your profs to administer the FCI in one of your grad classes.

  • 4 Paul Murray // Jul 7, 2008 at 7:25 pm

    “The first force is larger and thus the truck accelerates forward”

    No - surely not. The force applied by the trailer on the truck is *exactly* equal and opposite to that applied by the truck on the trailer.

    Matt replies: By “first force”, I meant the force of the ground on the tires. Sorry if the wording was unclear! In an idealized situation (ignoring friction, air resistance, etc) and just looking at the forces on the truck, there’s the force from the ground and the force from the trailer. The first is larger, thus the truck accelerates.

    But a sizeable component of that force is inertial reaction - precisely that force which you get from accelerating a mass. You could say that the acelleration “soaks up” any excess force that’s there until the rection is equal and opposite.

    The force of the road on the tyres is likewise matched by the forces applied by wind resistance, friction within the trivetrain (and other things), and the combied inertial reaction of the whole truck and trailer.

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