1. The problem statement, all variables and given/known data Im having difficulties with this on several problems. I understand work to be zero when there is either no displacement, no forces acting parallel to object or if friction and air resistance is not considered. Here is a simpler problem where i get the right answer if i set W = 0 but where i dont see WHY work done is zero: Harry is pulling a 25 pound (max pull) bow. The 1 oz. arrow is said to attain a speed of 140 feet/sec after release of the bowstring. If harry pulled the arrow back 18 inches prior to release, CONFIRM the arrow does leave the bow at 140 ft/s. 2. Relevant equations Potential Energy elastic = U = 1/2kx^2 where k = F/x Kinetic Energy = K = 1/2mv^2 Work = delta K + delta U 3. The attempt at a solution I set origin at where the string is at maximum pull so delta x is = 1.5 feet = 1.5 - 0 U initial = 1/2kx^2 k = F/x = ~16.667 U final = 0 K initial = 0 K final = 1/2mv^2 if work = force * delta x, then 25 * 1.5 = 37.5 Joules is my work. with W= delta K + delta U W = 37.5 J = 1/2mv^2 - 1/2kx (75 + kx)/m=v^2 v=240 ft/s but if i work this with w = 0 = 1/2mv^2 - 1/2kx v is verified at 140 ft/s I can see the work done on the string is zero, as it is pulled from an initial point and returns to the point, but how and why is work done on the arrow zero, if there is a displacement and a force of 25 lbs acting on it? Please help!