Problem: A 8 kg block is connected to a 3 kg block as shown; both are on greased inclines . The pulley is very light and frictionless. The static and kinetic coefficients of friction are 0.135 and 0.075, respectively. Find the speed after the combination has moved 45.0 cm if the system starts with a speed of 2.42 m/s.
Solution: This is one of those cases that is a little unwieldy with the energy balance method. We have to use reference levels for potential energy. But heights aren't given. From an earlier example in another module, we know that this system moves to the left. A 45 cm travel on the 68o incline means that the 3 kg block rises 45 sin68o = 41.7 cm. The 8 kg block (on the 32o incline) falls vertically 23.8 cm. Using the energy balance method, and realizing that some of the initial energy resources show up as heat (work due to friction Wf),
This simplifies to:
Returning to the module 5 example, we find that the frictional force on the 8 kg block is 4.99 N and the frictional force on the 3 kg block is 0.826 N. Notice that I'm not using the negative sign for frictional work here because its subtractive nature was taken into account by the way the energy balance equation was written? (When using the energy balance method, signs are never used!)
