(a) At a certain instant, a particle-like object is acted on by a force F with a

Question

(a) At a certain instant, a particle-like object is acted on by a force F with arrow = (4.5 N)i hat (1.8 N)j + (8.6 N)k while the object's velocity is v with arrow = (2.0 m/s)i hat + (4.0 m/s)k. What is the instantaneous rate at which the force does work on the object? (

b) At some other time, the velocity consists of only a y component. If the force is unchanged and the instantaneous power is 12 W, what is the velocity of the object? (Express your answer in vector form.)

(a) At a certain instant, a particle-like object is acted on by a force F (4.5 N) (1.8 N)j (8.6 N)k while the object's velocity is v (2.0 m/s (4.0 m/s)k. What is the instantaneous rate at which the force does work on the object? (b) At some other time, the velocity consists of only a y component. If the force is unchanged and the instantaneous power is -12 W, what is the velocity of the object? (Express your answer in vector form.) m/s

Explanation / Answer

Power is:

P = E/t = F . d /t = F . (d/t) = F . v

P = F . v

P = ( 4.5 i - 1.8j + 8.6 k ) . (-2 i + 4 k)

P = 4.5 x -2 + (-1.8) x 0 + 8.6 x 4 = -9 + 34.4 = 25.4 W

Hence, P = 25.4 W

b)P = Fy v

v = P/Fy

v = -12/-1.8 = 6.67 m/s

Hence, v = 6.67 m/s

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