(a) An object is subjected to the force F =3x3 z ı ^ + 5 z2k ^ N, wherex and z are in metres. The object can only move in thexz-plane.
         (i) Theobject moves from the origin by moving first along thex-axis to (a, 0) and then parallel to thez-axis to the point with coordinates (a,b). Howmuch work does the force do?
[2 marks]
         (ii) Theobject moves from the origin by moving first along thez-axis to (0,b) and then parallel to thex-axis to the point with coordinates (a,b). Howmuch work does the force do?
[2 marks]
         (iii) Isthis a conservative force?
[1 mark]
         (iv) Canthis force be expressed as the gradient of a potential? If so, givean expression for the potential. If not, give reasons why.
[2 marks]
(b) In the figure, we show a spring compressed by 85 cm. It isused to launch a physics student of mass 88 kg. The track isfrictionless until it starts up the incline. Assume that theacceleration of gravity is 9.8 m/s2. The student has acoefficient of kinetic friction of 0.23 on the 30oincline.
Figure 3 (If the image above does not appear,click here.)
         (i) Whatis the student's speed just after losing contact with thespring?
[3 marks]
         (ii) Oncethe student has reached the lowest point on the track, theycontinue back up the other side, slowed down by friction andgravity. How far does the student travel up the incline beforestopping?
[3 marks]
