A small rocket motor's thrust builds up and then dies away as F(t) = F_0

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Mechanics & Dynamical Systems · Calculus of change and accumulation

Mathematical Methods for Physics, Ch Accumulation: integration and the techniques that make it possible

Problem

A small rocket motor's thrust builds up and then dies away as

F(t) = F_0\,\frac{t}{\tau}\,e^{-t/\tau},

with

F_0 = 5.0\times10^3\,\mathrm{N}

and

\tau = 3.0\,\mathrm{s}

, and the motor is cut off at

T = 12\,\mathrm{s}

. (a) Name the slice of time you would add up to build the total impulse (change in momentum) delivered during the burn, and state its contribution. (b) Write the integral for the impulse

J

and evaluate it.

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