This is a problem that I came across in M2. I know that I'm wrong because I checked it using the normal SUVAT method, but the question specifically asks me to use the principle of conservation of energy and I can't get the right answer using that.
"The diagram shows a particle A of mass 2m which can move on a rough surface of a plane inclined at angle x to the horizontal, where sin x = 0.6. A second particle B of mass 5m hangs freely to a light inextensible string which passes over a smooth light pulley fixed at D. The other end of the string is attached to A. The coefficient of friction between A and the plane is 3/8. Particle B is initially hanging 2m above the ground ant A is 4m from D. When the system is released from rest with the string taut A moves up the greatest slope of the plane. When B has descended 1m the string breaks. By using the principle of conservation of energy calculate the total distance moved by A before it comes to rest."
You can probably visualise the problem from the description, D is the highest point of the triangle. This is my working.
The total potential energy lost by B by falling the 1m must be equal to the total potential energy gained by A plus the work done by A against the friction once it has reached its highest point.
The energy lost by B is mgh =5m*9.8*1=49mJ.
The work done by A against gravity is 2mgsinx*s where s is the distance travelled up the plane. The work done by A against friction is (3/8)2mgcosx*s. Simplifying (as cosx=0.8), 17.64ms=49m, s = 2.78.
However, the answer is 1.51 and I have got this result from doing this question the M1 dynamics way. What is wrong with my method? I'm assuming I've missed out an energy loss but I don't know where.