According to Hooke's Law, the force required to hold the spring stretched X m beyond its natural length is given by f(x) = kx, where k is the spring constant. Suppose that 2 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 47 cm. Find the exact value of k, in N/m. k = E m (a) How much work (in J) is needed to stretch the spring from 40 cm to 42 cm? (Round your answer to two decimal places.) :1 (b) How far beyond its natural length (in cm) will a force of 20 N keep the spring stretched? (Round your answer one decimal place.) :cm 1f the work required to stretch a spring 1 ft beyond its natural length is 15 ftlb, how much work (in ftlb) is needed to stretch it 6 in. beyond its natural length? Need Help? A cable that weighs 8 lb/ft is used to lift 700 lb of coal up a mine shaft 450 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let X be the distance in feet below the top of the shaft. Enter Xi* as Xi.) n n~>oo i= 1 Express the work as an integral. lSlE )dx Evaluate the integral. A chain lying on the ground is 10 m long and its mass is 60 kg. How much work (in J) is required to raise one end of the chain to a height of 4 m? (Use 9.8 m/s2 for g.) :1