A trucker needs to weigh a truck that is too long to fit on a platform scale. When the front wheels of the truck are run onto the scale, the scale reads [tex] W_1 [/tex]. When the rear wheels are run onto the scale so that the front wheels are off, it reads [tex] W_2 [/tex]. a) prove that the total wight of the truck is [tex] W_1 + W_2 [/tex]. b) prove that if the truck is loaded so that its center of gravity is halfway between the front and rear wheels, the total weight is [tex] 2W_1 [/tex].