Conceptual problem on Newton's Third Law

  1. Newton's Third Law states that for every action force, there is a reaction force.

    So take a classical problem with a basketball player. The earth has a gravitational force on the player, and thus player exerts an equal and opposite force on the earth. The player is stationary.

    My first question is, is this equal opposite force on the earth exerted by the player the normal force (yes, it would be numerically equivalent, but by definition)?

    Suppose the player decides to jump. Since there is a net force in play due to a certain net acceleration the player, things are no longer at an equilibrium. Does this mean that upon jumping, the player exerts more force on the earth (floor) than the earth exerts on the player? And if so, how is this variation from Newton's Third Law possible?

    Thank you beforehand.
  2. jcsd
  3. D H

    Staff: Mentor

    There are multiple forces acting on the basketball player in this scenario. That the player is stationary has nothing to do with the third law. The player is stationary because those multiple forces cancel. The Earth as a whole is gravitationally pulling the player downward, but at the same time the surface of the Earth is pushing the player upward via the normal force.

    So what are the third law reactions? That the Earth attracts the player gravitationally means that the player exerts an equal but opposite force on the Earth, directed upward. That the Earth pushes the player upward means that the player in turn pushes the Earth downward via the normal force.

    One final note: Unless the basketball player is at the North or South Pole, the downward gravitational force and the upward normal force do not quite cancel one another. The Earth is rotating about it's axis, and thus so is the player who is more or less stationary with respect to the surface of the Earth. The net force on the player must be just enough to place the player in uniform circular motion about the Earth's rotation axis.
  4. I'm slightly confused here. So we have two pairs of four forces, labeled 1,2,3,4:

    1. Gravitational force (field force) of earth on player, 2. gravitational force of player on earth

    3. The Earth holding the player up (Floor's contact force) on player, 4. the player in turn pushing the earth down due to normal force

    Isn't 1 the same as 4, or directly caused by 4? And my question point about being stationary was meant to simply exemplify the fact that all the forces appeared to cancel out, leading to my question about the player jumping.
  5. mfb

    Staff: Mentor


    3 and 4 can be seen as caused by 1 and 2. They are not the same.

    No, the forces between player and earth (via the ground, 3 and 4 in your list) both increase and get larger than the gravitational forces (1 and 2). The forces on the objects are no longer balanced and they will accelerate. The earth starts to move backwards/downwards a tiny bit.
  6. First part: There are two action-reaction pairs at play when the person is stationary. The first pair consists of the force that the player's feet exert on the ground and the equal and opposite reaction force that the ground exerts on the feet. The second pair is the gravitational force exerted by the Earth on the player and the equal and opposite gravitational reaction force that the player exerts on the Earth (every object in the universe attracts every other object, according to Newton's universal gravitation). These pairs of forces have essentially nothing to do with each other.

    It just so happens that, in this example, the upward/normal force exerted by the floor on the person exactly balances the downward pull of the Earth. So, the guy stays stationary.

    Second part: When the player goes to jump, he uses his legs to exert a greater force on the ground than is present when he is just standing. The reaction force, equal and opposite, that the ground exerts on the person is greater than the downward force of gravity, accelerating the player upwards.

    It's very important to realize which forces are acting where, and which objects are providing them. You mixed up the action/reaction forces in your introduction of the problem.
    1 person likes this.
  7. NO! They are not the same forces. They are in fact causally related, but that has no bearing on the resultant acceleration, or lack thereof, of the object in question (the person). Forces 1 and 3 are equal and opposite, but not because of action/reaction, just because that's the way it is in this particular situation.
  8. Hi Conservation,

    Forces are always caused by some sort of interaction between two objects. When two objects interact through gravity then there will be a gravitational force from each object on the other object. When two objects interact through contact then there will be a contact force from each object on the other object. These forces are equal and opposite and form 3rd law pairs.

    So the important characteristics of a 3rd law pair are
    1) they each are of the same "kind"
    2) they each act on different objects

    If the player is at rest then the gravitational force is equal and opposite to the normal force, but one is a gravitational force and the other is a contact force and they are acting on the same object. So they are not a third law pair because they don't meet those two characteristics. Gravitational forces and contact forces are not the same "kind" of forces, and the player is a single object.
  9. I see; thanks for all the replies. I now see how the two pairs of forces are separate, so, just to sum up for confirmation:

    There are four forces acting on the basketball player.

    At rest, the pair of gravitational forces (1 earth on player, 2 player on earth) exist along with pair of contact forces (3 floor on player, 4 player on floor). Since the player is not exerting any extra force on the floor aka earth, the force of the player on floor equals the gravitational force on earth. Hence, Force 1=Force 2 due to Newton's third law, Force 1=Force 4 due to no further exertion of force by the player on the floor, and Force 3=Force 4 due to Newton's third law.

    However, while jumping, the player exerts more force on the floor than previously, which only accounted for his weight. Force 1 no longer equals force 4; force 4 is the sum of the force applied by the player and the weight of the player. However, 1=2 and 3=4 still hold due to Newton's third law. Thus, Force 3 (the floor's upward contact force) becomes greater than force 1, allowing the player to "defy gravity" momentarily.

    At least, I think that's how that works...right?
  10. mfb

    Staff: Mentor

    Only 2. The other two are acting on earth.
  11. Seems like you got it!
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