Question and Answers Forum

All Questions      Topic List

Vector Calculus Questions

Previous in All Question      Next in All Question      

Previous in Vector Calculus      Next in Vector Calculus      

Question Number 122189 by physicstutes last updated on 14/Nov/20

Given that the forces F_1 , F_2 and F_3 have position vectors r_1 , r_2 and r_3 . Where, F_1 = (2i + 3i + k) N r_1 = (i + 2k) m F_2 = (3i + 2i + 5k) N r_2 = (2i − 4j + k) m F_3 = (−5i−5j −6k) N r_3 = (4i + 3j + 2k) m (a) Find the moment of F_1 about (2i + 3j + 4k) m. (b) Show that this system of forces reduces to a couple, G, and find the magnitude of this couple. (c) Check if F_1 and F_2 are concurrent.

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{forces}\:\boldsymbol{\mathrm{F}}_{\mathrm{1}} ,\:\boldsymbol{\mathrm{F}}_{\mathrm{2}} \:\mathrm{and}\:\boldsymbol{\mathrm{F}}_{\mathrm{3}} \:\mathrm{have}\:\mathrm{position}\:\mathrm{vectors} \\ $$$$\:\boldsymbol{\mathrm{r}}_{\mathrm{1}} ,\:\boldsymbol{\mathrm{r}}_{\mathrm{2}} \:\mathrm{and}\:\boldsymbol{\mathrm{r}}_{\mathrm{3}} .\:\mathrm{Where}, \\ $$$$\:\boldsymbol{\mathrm{F}}_{\mathrm{1}} \:=\:\left(\mathrm{2}\boldsymbol{\mathrm{i}}\:+\:\mathrm{3}\boldsymbol{\mathrm{i}}\:+\:\boldsymbol{\mathrm{k}}\right)\:\mathrm{N}\:\:\:\:\:\:\boldsymbol{\mathrm{r}}_{\mathrm{1}} \:=\:\left(\boldsymbol{\mathrm{i}}\:+\:\mathrm{2}\boldsymbol{\mathrm{k}}\right)\:\mathrm{m} \\ $$$$\:\:\boldsymbol{\mathrm{F}}_{\mathrm{2}} \:=\:\left(\mathrm{3}\boldsymbol{\mathrm{i}}\:+\:\mathrm{2}\boldsymbol{\mathrm{i}}\:+\:\mathrm{5}\boldsymbol{\mathrm{k}}\right)\:\mathrm{N}\:\:\:\:\boldsymbol{\mathrm{r}}_{\mathrm{2}} \:=\:\left(\mathrm{2}\boldsymbol{\mathrm{i}}\:−\:\mathrm{4}\boldsymbol{\mathrm{j}}\:+\:\boldsymbol{\mathrm{k}}\right)\:\mathrm{m} \\ $$$$\:\boldsymbol{\mathrm{F}}_{\mathrm{3}} \:=\:\left(−\mathrm{5}\boldsymbol{\mathrm{i}}−\mathrm{5}\boldsymbol{\mathrm{j}}\:−\mathrm{6}\boldsymbol{\mathrm{k}}\right)\:\mathrm{N}\:\:\:\:\boldsymbol{\mathrm{r}}_{\mathrm{3}} \:=\:\left(\mathrm{4}\boldsymbol{\mathrm{i}}\:+\:\mathrm{3}\boldsymbol{\mathrm{j}}\:+\:\mathrm{2}\boldsymbol{\mathrm{k}}\right)\:\mathrm{m} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{moment}\:\mathrm{of}\:\boldsymbol{\mathrm{F}}_{\mathrm{1}} \:\mathrm{about}\:\left(\mathrm{2}\boldsymbol{\mathrm{i}}\:+\:\mathrm{3}\boldsymbol{\mathrm{j}}\:+\:\mathrm{4}\boldsymbol{\mathrm{k}}\right)\:\mathrm{m}. \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Show}\:\mathrm{that}\:\mathrm{this}\:\mathrm{system}\:\mathrm{of}\:\mathrm{forces}\:\mathrm{reduces}\:\mathrm{to}\:\mathrm{a}\:\mathrm{couple},\:\boldsymbol{\mathrm{G}},\: \\ $$$$\mathrm{and}\:\mathrm{find}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{this}\:\mathrm{couple}. \\ $$$$\left(\mathrm{c}\right)\:\mathrm{Check}\:\mathrm{if}\:\boldsymbol{\mathrm{F}}_{\mathrm{1}} \:\mathrm{and}\:\boldsymbol{\mathrm{F}}_{\mathrm{2}} \:\mathrm{are}\:\mathrm{concurrent}. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com