(a) At a certain instant, a particle-like object is acted onby a force F = (4.0N
ID: 1668180 • Letter: #
Question
(a) At a certain instant, a particle-like object is acted onby a force F = (4.0N)i - (1.0 N)j +(8.0 N)k while the object'svelocity is v = - (2.0 m/s)i + (4.0 m/s)k .What is the instantaneous rate at which the force does work on theobject?W
(b) At some other time, the velocity consists of only aj component. If the force is unchanged, and theinstantaneous power is -12 W, what is the velocity of the objectjust then?
m/sj
(a) At a certain instant, a particle-like object is acted onby a force F = (4.0N)i - (1.0 N)j +(8.0 N)k while the object'svelocity is v = - (2.0 m/s)i + (4.0 m/s)k .What is the instantaneous rate at which the force does work on theobject?
W
(b) At some other time, the velocity consists of only aj component. If the force is unchanged, and theinstantaneous power is -12 W, what is the velocity of the objectjust then?
m/sj
Explanation / Answer
a. Rate of doingwork = power P = F. v P = (4.0i^ - 1.0j^ + 8.0k^) . ( - 2.0i^ + 4.0k^) = -8.0 i^.i^ + 32.0k^. k^ = 24.0 W (as i^ . i^ = j^ . j^ =k^.k^ = 1 & i^.j^ = j^.k^ = k^.i^ = 0) P = (4.0i^ - 1.0j^ + 8.0k^) . ( - 2.0i^ + 4.0k^) = -8.0 i^.i^ + 32.0k^. k^ = 24.0 W (as i^ . i^ = j^ . j^ =k^.k^ = 1 & i^.j^ = j^.k^ = k^.i^ = 0) b. -12 = (4.0i^ - 1.0j^ + 8.0k^) . ( v j^) = -1.0 * v j^ . j^ v = 12/ 1.0 = 12 hence v = (12j^) m/s v = 12/ 1.0 = 12 hence v = (12j^) m/sRelated Questions
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