Menu Close

A-particle-of-mass-2kg-moves-in-a-force-field-depending-on-a-time-t-given-by-F-24t-2-i-36t-16-j-12tk-assuming-that-at-t-0-the-particle-is-located-at-r-0-3i-j-4k-and-has-v-0-




Question Number 27427 by tawa tawa last updated on 06/Jan/18
A particle of mass 2kg moves in a force field depending on a time t given by  F = 24t^2 i + (36t − 16)j − 12tk   assuming that at t = 0 the particle is located  at  r_0  = 3i − j + 4k  and  has   v_0  = 6i + 5j − 8k. Find  (a) Velocity at any time t  (b) Position at any time t  (c) τ (torgue) at any time t  (d) Angular momentum at any time t above the Origin
$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2kg}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{force}\:\mathrm{field}\:\mathrm{depending}\:\mathrm{on}\:\mathrm{a}\:\mathrm{time}\:\mathrm{t}\:\mathrm{given}\:\mathrm{by} \\ $$$$\mathrm{F}\:=\:\mathrm{24t}^{\mathrm{2}} \mathrm{i}\:+\:\left(\mathrm{36t}\:−\:\mathrm{16}\right)\mathrm{j}\:−\:\mathrm{12tk}\:\:\:\mathrm{assuming}\:\mathrm{that}\:\mathrm{at}\:\mathrm{t}\:=\:\mathrm{0}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{located} \\ $$$$\mathrm{at}\:\:\mathrm{r}_{\mathrm{0}} \:=\:\mathrm{3i}\:−\:\mathrm{j}\:+\:\mathrm{4k}\:\:\mathrm{and}\:\:\mathrm{has}\:\:\:\mathrm{v}_{\mathrm{0}} \:=\:\mathrm{6i}\:+\:\mathrm{5j}\:−\:\mathrm{8k}.\:\mathrm{Find} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Velocity}\:\mathrm{at}\:\mathrm{any}\:\mathrm{time}\:\mathrm{t} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Position}\:\mathrm{at}\:\mathrm{any}\:\mathrm{time}\:\mathrm{t} \\ $$$$\left(\mathrm{c}\right)\:\tau\:\left(\mathrm{torgue}\right)\:\mathrm{at}\:\mathrm{any}\:\mathrm{time}\:\mathrm{t} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{Angular}\:\mathrm{momentum}\:\mathrm{at}\:\mathrm{any}\:\mathrm{time}\:\mathrm{t}\:\mathrm{above}\:\mathrm{the}\:\mathrm{Origin} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *