MATH1014 T02A / T02B / T02C / T02D Tutorial Exercise (Week 5) Answers W= Fsfor a constant force W=Fdsm= ρVfor an evenly distributed mass m=dVPE= mghfor a constant mass PE=ghdVIn this exercise, take g= 9.8 Nkg–1. 1.Suppose a force of 15 N is required to stretch and hold a spring 0.25 m from its equilibrium position. (a)Assuming the spring obeys Hooke’s law F= kx, find the spring constant k. 60 Nm–1(b)How much work is required to compress the spring 0.2 m from its equilibrium position? 1.2 J (c)How much additional work is required to stretch the spring 0.3 m further if it has already been stretched 0.25 m from its equilibrium position? 7.2 J 2.A spring requires a force of 50 N to stretch 0.1 m from its equilibrium position. Write the integral that represents the work required to stretch the spring 0.4 m from its equilibrium position. Assume Hooke’s law is obeyed. 4.00500xdx3.Two bars of length Lhave densities ρ1(x) = 4e–xand ρ2(x) = 6e–2xfor 0 ≤x≤L.