Question

(a) An object is subjected to the force F = 3x³ z ı ^ + 5 z^{2k ^} N, where x and z are in metres. The object can only move in the xz-plane.

          (i) The object moves from the origin by moving first along the x-axis to (a, 0) and then parallel to the z-axis to the point with coordinates (a,b). How much work does the force do?

[2 marks]

          (ii) The object moves from the origin by moving first along the z-axis to (0,b) and then parallel to the x-axis to the point with coordinates (a,b). How much work does the force do?

[2 marks]

          (iii) Is this a conservative force?

[1 mark]

          (iv) Can this force be expressed as the gradient of a potential? If so, give an expression for the potential. If not, give reasons why.

[2 marks]

(b) In the figure, we show a spring compressed by 85 cm. It is used to launch a physics student of mass 88 kg. The track is frictionless until it starts up the incline. Assume that the acceleration of gravity is 9.8 m/s². The student has a coefficient of kinetic friction of 0.23 on the 30^o incline.

Figure 3 (If the image above does not appear, click here.)

          (i) What is the student's speed just after losing contact with the spring?

[3 marks]

          (ii) Once the student has reached the lowest point on the track, they continue back up the other side, slowed down by friction and gravity. How far does the student travel up the incline before stopping?

[3 marks]

Answer 1