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Consider an object of mass m moving in f...

Consider an object of mass m moving in free space with velocity given by ` vec(v) = v_(0) cos omega t hat (i) +v_(0) sin omegat hat (j) ` . `. Here `v_(0) and omega` are constants and t represents time. calculate force acting on object and angle between force and momentum.

Text Solution

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(1) Let us calculate the force acting on it.
As ` vec(p) = mvec(v) , ` we have
` vec(p) = mv_(0)[cos omega vec(t) + sin omega t hat (j)]`
` rArr (dvec(p))/(dt) = mv_(0) [-sin omega t xx omega hat(i) + cos omegat xx omega hat(j)]`
` :. vec (F) = mv_(0) [ -sin omegat hat(i) + cos omegat hat(j)]`
(2) Let us calculate the angle between force and momrntum .
` vec(F) . vec(p) = |vecF| | vec(p)| cos theta `
` rArr |vec(F)| |vec(p)| cos theta = (mv_(0)omega) (mv_(0))[-sin omegat cos omegat + sin omegat cos omegat]=0`
As ` vec (F) .vec(p) = 0 rArr theta = 90^(@) :. vec(F) bot vec (p)`
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