A certain spring is found not to obey Hooke's law; it exerts a restoring force Fx(x)=−αx−βx2Fx(x)=−αx−βx2 if it is stretched or compressed, where α=60.0N/mα=60.0N/m and β=18.0N/m2β=18.0N/m2. The mass of the spring is negligible.

A. Calculate the potential energy function

U(x) for this spring. Let U=0 when x=0.

Express your answer in terms of x.

B. An object with mass

0.900kg on a frictionless, horizontal surface is attached to this spring, pulled a distance 1.00m to the right (the + x - direction) to stretch the spring, and released. What is the speed of the object when it is 0.50m to the right of the x=0 equilibrium position?

Amerry-go-round of radius r, shown in the figure, is rotating at constant angular speed. the friction in its bearings is so small that it can be ignored. a sandbag of mass m is dropped onto the merry-go-round, at a position designated by r. the sandbag does not slip or roll upon contact with the merry-go-round. how would you rank the following different combinations of m and r on the basis of the angular speed of the merry-go-round after the sandbag "sticks" to the merry-go-round from largest to smallest. a) m = 10kg, r = 0.25r b) m = 20kg, r = 0.25r c) m = 10kg, r = 0.50r d) m = 10kg, r = 1.0r e) m = 15kg, r = 0.75r f) m = 40kg, r = 0.25r