1. The problem statement, all variables and given/known data I am trying to understand the law of conservation of energy from a very general perspective but coming across some issues. I am using the equation mentioned at end of this post, which is true for a system with no heat flows into or out of the system. In two situations described below,if the applied force and friction force are both non-conservative then using the general equation below, the change in internal energy of block should be negative of the sum of work done by applied force and friction force. This makes sense in situation 1 where internal energy increases but not in situation 2 where I am getting that internal energy of block decreases. I am sure I am making a mistake somewhere but cannot see it. SITUATION 1 ( without applied force) A block of mass 1 kg moving at 10 m/s on a rough horizontal surface with a coefficient of friction of 0.25 is brought to rest by friction. We will focus from initial instant when it's speed is 10 m/s to when it comes to rest. SITUATION 2 ( with an applied force) A force of 200 N is applied to a block of 1 kg mass on a rough horizontal surface with a coefficient of friction of 0.25. This causes the block to move in the direction of force. We will focus on first 10 m of the block's motion. Question Does this reasoning for situation 2 sound correct if it's assumed that no heat flows into and out of the block? 2. Relevant equation General equation for conservation of energy without heat flows 3. The attempt at a solution SITUATION 1 ( without applied force) The work done by friction force in this case is .5 x 1 x 102 = 50 J. If we use the equation given at end of this post then the work done by non-conservative force of friction is converted to internal energy of the block i.e. internal energy change = - (-50) = + 50 J which causes internal energy of block to rise. SITUATION 2 ( with an applied force) For the first 10 m, work done by the applied force = + 200 x 10 = + 2000 J and work done by friction force is = - 1 x 10 X .25 = - 2.5 J. So, net work done by non-conservative forces is 2000 - 2.5 = + 1997.5 J. If the equation given below is true then change in internal energy is - 1997.5 J which means the internal energy of the block has decreased by the end of this 10 m distance.