A fisherman in a boat is using a "10-lb test" fishing line. This means that the line can exert a force of 45 N without Breaking (1 lb=4.45 N). (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (h) If he accelerates the fish upward at 2.0 m/s2 what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-lb test line? Why or why not?
Solution 85GP: We have to determine the heaviest fish can be pulled out of water at a constant speed and at constant acceleration. In the third part, we have to find whether it is possible to land a 15lb trout on 10 lb test line. Step 1 of 6 Concept: Newton’s second law: The net force F acting on an object of mass m produces an acceleration a in that object. Mathematically, F= ma. Tension is the internal developed in the test line, which depends upon the application and magnitude of force applied. Free body diagram of a body gives the diagrammatical representation of all the forces acting on the body in terms of magnitude and diagram, under the given situation. Step 2 of 6 Figure below shows the free body diagram of the fish m Mass of the fish mg Weight of the fish F Tension in the test line T ma Net force acting on the fish a Acceleration of the fish Taking all the forces in the upward direction to be positive and vice versa. Step 3 of 6 A] Heaviest fish can be pulled out of water at a constant speed The tension in the rope is acting along the rope in the upward direction. The fish is being pulled upward vertically as shown in the free-body diagram and the weight of the fish is acting vertically downward. By applying Newton’s Second Law, we get, F mg = ma T As the fish is being pulled out at the constant speed, therefore its acceleration is a = 0 m/s . F T mg = 0 mg = F T As the line can exert a maximum tension of 45N without breaking, therefore the maximum weight of the fish that the 10lb test line can support is 45N. mg = 45 = 10 lb m = 45 = 4.6 kg 9.8 The heaviest fish can be pulled out of water at a constant speed is of mass m = 4.6 kg and weight 45 N.