many types of mattresses exist, from inner-springs to memory foam and non-elastic material. While traditional mattress a built with a set of internal springs, the desgins have continually changed. one more recent form of the innner spring system is to have many parallel spring sets, each able to compress indicvidually if pressure is applied to it. These can be described as "a flexible outer coil... [and] a tightly wound inner coil ". Consider a single coil setm with the shorter, stiffer spring inset inside the coils of the first spring, allowing the more flexible and longer to outer spring to compress some 10.0 cm before the second psring does. ignore the effects of the mass of any other comonents of the bed resting on top of the spring. (a) Consider the situation where this set of springs has to support a 1/10 the weight of a child of mass 20.0 kg. What is the minimum stiffness of the outer spring if the second, stiffer spring does not compress. (b) A 60.0-kg person now lays on the bed, with a single coil now supporting 1/20 of their weight. If the second spring is 4 times a stiff as the first spring, how far does the second spring compress? (c) by what factor is the work done by the first spring larger than the work done by the second spring?