When do one use the principle of conservation of mechanical energy to find the velocity of a mass, and when would you use the sum of forces equals to the mass times acceleration, and there after use a ds=v dv in order to find the velocity. The specific question related to this is a spring fixed to a mass which is pulled up a slope by a constant force. They want the final velocity. I already have the force in terms of distance that the spring applies of the mass. I have the constant force etc. I used sum of F's = ma and a ds = v dv in order to find velocity. In the memo however They used conservation of energy: T1 +V1 +U1-2 = T2 +V2. My answer is different to the memo. Should'nt the answer be the same? and if not? Whats the two cases that splits these two methods of approach?