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# 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?

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- Big DaddyLv 77 years agoFavorite Answer
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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- JullyWumLv 77 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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