Newton's laws and momentum

MDCAT Physics · Physics · Force and motion. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Newton's laws link force and motion. A body keeps its state of rest or uniform velocity unless a net force acts on it. This resistance to change is inertia, and it depends only on mass. A net force gives an acceleration in its own direction. Forces always come in equal and opposite pairs that act on two different bodies.

Momentum is mass × velocity and is a vector. A force acting for a time changes the momentum; force × time is called impulse. A longer time for the same change of momentum means a smaller force.

When no external force acts on a system, its total momentum stays the same in every collision. Kinetic energy is conserved only in an elastic collision.

Rules to remember

Common mistake

Students forget that momentum is a vector. When a body reverses direction, one velocity must be negative, so the change in momentum is larger than either momentum alone.

Worked example

A 0.15 kg ball moving at 20 m s−1 is hit straight back at 30 m s−1. The bat touches the ball for 0.010 s. Find the average force on the ball.

  1. Take the final direction as positive: u = −20 m s−1, v = +30 m s−1.
  2. Change in momentum = m(v − u) = 0.15 × (30 − (−20)) = 0.15 × 50 = 7.5 kg m s−1.
  3. Force = change in momentum ÷ time = 7.5 ÷ 0.010 = 750 N.

Answer: 750 N, in the direction the ball leaves the bat.

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