A. Work and Kinetic Energy The work W done by a constant force F acting on an object undergoing a straight-line displacement d is W = F.d.cos0 where 0 is the smallest angle between the force F and the displacement d when the vectors are placed tail-to-tail. The work energy theorem states that the change in kinetic energy of a system (AK ) is equal to the total (net) work done by all external forces on the system: We = AK = Ky- K; 1. The two ropes shown in the bird's-eye view of the diagram are used to drag a crate 3.00 m horizontally across a rough floor. The tensions in the two ropes are 71= 402 N and To = 275 N; the magnitude of the kinetic friction force is f* = 500 N. a) What is the direction of the displacement vector d whose magnitude is 3.00 m? b) How much work is done by rope Ti? c) How much work is done by rope T? d) How much work is done by kinetic friction f.? e) What is the total (net) work done on the crate? {+348 /}2. Let's imagine the following: Benedict's job at the amusement park is to slow down and bring to a stop the boats in a log ride. A boat and its riders have a total mass of m and drift with an initial speed of vi. Let's assume that Benedict applies a constant force F in order to bring the boat to a final speed of vr. a) If the boat has a mass of 1200 kg and an initial speed of 1.20 m/s, how much total work is done on the boat to slow it to 0.60 m/s (half its initial speed)? {-648 J) b) How much total work is done on the boat to bring it to rest from its initial speed of 1.20 m/s? {-864 /} c) What average power is expended in bringing the boat to rest in 8.00 s? 3. A catapult launcher on an aircraft carrier accelerates a jet from rest to 72.0 m/s. The work done by the catapult during the launch is 76.0 MJ. During the launch, forces other than the force exerted by the catapult on the jet are negligible, that is, the total work done on the jet is due solely to the catapult. a) What is the mass of the jet? (2.93 x 10*kg] b) If the jet is in contact with the catapult for 2.00 s, what is the power output of the catapult? (36.0 MW)