Answer to Question #173068 in Physics for abcdef

Question

1) A physics student observes a frictionless pendulum with a pendulum bob of mass 0.10-kilogram as shown in the diagram below. The pendulum swings freely from rest at an unknown height into a spring with a spring constant of 15 Newtons per meter. The initial length of the spring is measured to be 0.25 meters. The force exerted on the spring by the pendulum bob causes the object to come to a complete rest as it compresses the spring. The student records the final length of the spring to be 0.20 meters long.

Calculate the initial height of the pendulum swing.

Answer 1

$$mgh=0.5k(x_1)^2-0.5k(x_2)^2\\(0.1)(9.8)h=0.5(15)(0.25)^2-0.5(15)(0.2)^2\\h=0.17\ m$$