In a machine a cylinder with a mass of 80.0 g is pushed down into a hole with a spring at the

Question

bottom as shown in Figure 1. When the spring is uncompressed the cylinder rests on top of it with
its end just at the entrance to the hole. The cylinder is pushed by a rod which is angled at 30◦ as
shown. The rod exerts a force of 10.0 N parallel to the line that the rod points along. The walls of
the hole are well oiled so you can ignore friction. The spring has a stiffness of 1200 N/m. Getting
the timing of the machine right requires that we know the speed of the cylinder when the spring is
6.00 cm long as shown.
(a) Choose your system and define your axes clearly.
(b) Draw an energy bar chart for the situation.
(c) Solve for the speed of the cylinder when the spring is 6.00 cm long.
(d) Calculate the height of each of the “bars” in your energy bar chart. Is there one of the types
of energy that you used which is very small compared to the others? Recalculate the answer
to c) neglecting this contribution to see how good the approximation is. (In practice when
objects in machines are moving fast and there are spring forces involved the approximation
you have just found is a very good approximation.)