CAT 1 SPH:2200 MECHANICS II.
1)Given two vectors functions;
A=yz2i-3xz2j + 2xyzk and B=3xi + 4 zj – xyk and a scalar function ?=xyz
Find: i)(A×?)?
ii)B•??×A
All at a point with coordinates (-1, 1, 1) (6mrks)
2)(i)A particle is moving in a straight line and its distance (S) meters from a fixed point in the line after t seconds is given by S=12t-15t2 + 4 t3 calculate:
-the speed and magnitude of acceleration of the particle after 3 seconds.
-the distance traveled between the two times when the speed is instantaneously zero. ( zero).
(ii)The vectors A and B are given by: A=2i + 3j + 7k , B=-I + 6j – 5k
Calculate; i)A×B ii) A•B iii) angle between A and B.(6 marks)
3)(i)Define a conservative force field.(1 mrk)
(ii)A conservative force field may be expressed as negative gradient of potential F= -??V. Show that ?? × F = 0
( iii) Show that a force field defined by;
F =(6xyz + z2 )i + 3x2zj + (3x2y + 2 xz )k is a conservative force field.(4 mrks)
(iv)Determine the associated potential (?) to the above force field in (a) (ii) (3 mrks )
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