Question 5 You have landed on the planet Hephaestia, where the gravitational constant of acceleration ghas a different value than it does on Earth. Your spaceship contains a device which may be used to find the value of gon any planet. In this device a particle A with mass mAkg is connected by a light inextensible string to a light scale-pan. A force meter Cwith mass mekg is placed in the scale- pan, and a small block Bwith mass mg kg is placed on top of C. A is held in place on a rough plane angled at 0to the horizontal, where the coefficient of friction between A and the plane is . The string passes over a smooth light pulley fixed at the top of the plane so that the scale-pan is hanging vertically downwards as shown in the diagram below: A B C 0 T With the string between A and the pulley lying along a line of greatest slope of the plane, A is projected down the plane with a velocity of vms-1 parallel to the string. After a time of seconds the system comes momentarily to rest, and then the scale- pan begins to descend under the force of gravity, pulling mass A up the slope behind it. When the scale-pan is initially moving upwards, the force exerted by Bon Cis denoted by FBCT. When the scale-pan begins to descend, the force exerted by Bon Cis denoted by FBC. The force meter is only able to record the difference AF between these two values, where AF = FBC - FBC. Show that 2m AB AF= gu cos 0 A m+mB+mc [11 marks]