Question

Correctly state Newton's third Law of Motion in your own words.
Describe what is the goal of an NFL Defender, and how would he use Newton’s Third Law to reach that goal.
How is momentum determined in football? Give the equation used, and explain it.
Explain the Law of Conservation of Momentum.
How does Newton’s Cradle explain momentum and how is this depicted by players in the game?

Answer 1

1) Newton’s Third Law of Motion (in my own words)
- Whenever one object pushes or pulls on a second object, the second object pushes or pulls back on the first with the same magnitude of force but in the opposite direction.
- In short: forces come in equal-and-opposite pairs; you cannot exert a force without receiving a reaction force.

2) Goal of an NFL defender and how Newton’s Third Law helps
- Goal: remove the ball from the offense’s control — most commonly by stopping (slowing or arresting) the ball carrier’s forward motion, forcing a tackle, fumble, or loss of yards.
- How Newton’s Third Law is used:
- To accelerate into a play the defender must push against the ground with their foot. The ground pushes back (reaction force) and propels the defender forward toward the ball carrier.
- During a tackle the defender applies a force to the runner. The runner applies an equal and opposite force back on the defender. The resulting accelerations depend on each player’s mass and how they apply force (direction, leverage, and time of contact).
- Effective tackling often uses body positioning and bracing (using legs, hips, shoulders) so the defender can direct the reaction forces to change the runner’s momentum (e.g., stop or redirect them) rather than being pushed off balance.

3) How momentum is determined in football — equation and explanation
- Equation: momentum p = m v
- p is momentum (a vector), m is mass, v is velocity. Units: kg·m/s (or slugs·ft/s).
- Explanation: momentum quantifies how hard an object is to stop. A heavier player (larger m) or a faster player (larger v) has more momentum. When two players collide, their momenta determine how their velocities change during and after contact.

- Useful related equation (impulse relation): Δp = F Δt
- Change in momentum (Δp) equals the net force F applied times the contact time Δt. A defender can reduce the runner’s momentum by applying a large force or by applying force over a longer contact time (wrapping and driving through the tackle).

4) Law of Conservation of Momentum
- Statement: For an isolated system with no net external force, the total momentum of the system stays constant in time. Mathematically, Σp_initial = Σp_final.
- In collisions this means the vector sum of momenta of all interacting bodies before impact equals the sum after impact.
- Caveats for football: the player–player system is only approximately isolated for the brief collision period; external forces (ground friction, other players, air resistance) and inelastic processes (energy loss to deformation, heat) mean perfect conservation often does not hold for longer times or when including the ground.

5) Newton’s Cradle, momentum, and the analogy to football
- Newton’s Cradle (the row of swinging balls) shows how momentum and kinetic energy can be transferred through a chain of elastic collisions: when one ball strikes the next, the impulse and momentum travel through the line so that the last ball swings out with nearly the same momentum as the first had. In an ideal cradle the collisions are elastic, so both momentum and kinetic energy are (approximately) conserved among the balls.
- How that maps to football:
- Direct transfer: in some plays a shove or push at one spot of the line transmits force through bodies so that the effect (movement) shows up at the far end — like a shove in the trench where pressure is transmitted through pads and bodies. This is analogous to momentum being passed along in Newton’s Cradle.
- Important difference: most football collisions are highly inelastic — players deform, grab, fall and dissipate kinetic energy. So momentum might be redistributed among the players and the ground, while kinetic energy is lost to heat, body deformation, and sound.
- Tackling example: a defender striking a ball carrier transfers momentum to the carrier; if the defender and carrier stick together (or fall together), that is a perfectly inelastic-like outcome where momentum is conserved for the two-body system but kinetic energy is not. If the defender bounces the runner back, more momentum is transferred out of the runner and into other bodies or the ground.

Short practical points for defenders (physics applied)
- To stop a high-momentum runner, either apply a larger net force (stronger hit) or increase contact time (wrap and drive) to produce the necessary impulse.
- Use the ground: push off the turf to create larger reaction forces and reach the ball carrier faster.
- Control direction: since momentum is a vector, redirecting a runner’s velocity (rather than trying to stop it instantly) can be more effective and safer.

If you want, I can show a numeric example (compute momenta of two players and the result of an elastic vs. inelastic collision) to illustrate these concepts.