85.5 applications of Newton's law Example 1: A submarine is sinking in the sea. If the buoyancy is F, the kinetic friction isf=-kAv, where A is the area of the cross section of the submarine Find the function of the speed of the submarine with respect to the time 85.5 applications of Newtons law Solution: y, total=-F-kAv+ mg mas d y mg v〓n d t mdv d t 0 mg -F-kAv 0在mgFk4p) d t mg-F-k4ν ln(mg-F-k4ν 410 Example 1: A submarine is sinking in the sea. If the buoyancy is , the kinetic friction is , where A is the area of the cross section of the submarine. Find the function of the speed of the submarine with respect to the time. F r f kAv r r = − §5.5 applications of Newton’s law c F r f r W r o y ∫ ∫ = − − − − = v t t mg F kAv m v t v mg F kAv m 0 0 d d d d ∫ ∫ = − − v − t t mg F kAv mg-F-kAv kA m 0 0 d d( ) t v mg-F-kAv kA m − = 0 ln( ) Solution: Fy,total = −F − kAv + mg = ma y §5.5 applications of Newton’s law