(i)Define a conservative force field.( 1 mark)
(ii)A conservative force may be expressed as:
?(?-F )=- ?(?-? ?(?-V ))
Show that for such a force, ??×F = 0 (4 marks)
(iii)Show that a force field defined by;
F=(6xyz + z2)i + 3 x2yz j + (3 x2y + 2xz)k is a conservative force field. (3 marks)
(iv) Determine the associated potential (V) to the above force field in (a) (iii) (4 marks)
(b) A particle of mass 3 units moves in a force field depending on time t given by;
F=12t2i +(6t – 3)j -3tk .If its position vactor at time t=0 seconds is given by; ro= 2i + j -2 k and its initial velocity at this instant given by; Vo=4i +5 j + 3k
Detemine
Its velocity and position at any time(t).(4 marks)
Torque and angular momentum about the origin for the particle at time(t)
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