If resultant force is directly proportional to rate of change of momentum what is constant (k)?

Because if F is proportional to d(mv)/dt then F=k(d(mv)/dt), what is k?

2 Answers

  • 7 years ago
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    Any non-zero value of k will yield an equation where F is directly proportional to d(mv)/dt.

    F = k d(mv)/dt

    F = m k d(v)/dt

    F = m k a

    k is just a proportionality constant so that the units of force, mass and acceleration can be compared. If you use SI units (newtons, kilograms, meters-per-second-squared), then k is 1.

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  • 7 years ago

    k depends on how you define the Newton unit of force.

    From Newton 2nd law force F ∝ (mv -mu)/t

    F = km {(v-u)/t}

    F = kma

    By defining the Newton as .. "that (net) force that causes a 1kg mass to accelerate at 1 m/s² " k has the value 1

    k = F/ma .. 1N/(1kg x 1m/s²) = 1

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