Consider three vectors: A~, B~ , and C~ . These vectors are related by: A~ + B~ = 5C~
A~ − B~ = 3C~
Vector C~ has components Cx = 2 and Cy = 4. Find the x- and y- components of A~ and B~ (e. g. find Ax, Ay, Bx, and By).

The rigid beam is supported by the three suspender bars. bars ab and ef are made of aluminum and bar cd is made of steel. if each bar has a cross-sectional area of 450 mm2, determine the maximum value of p if the allowable stress is (σallow)st = 200 mpa for the steel and ( σallow)al = 150 mpa for the aluminum. est = 200 gpa and eal = 70 gpa.

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.

At the negative terminal of the battery the electron has electric potential energy. what happens to this energy as the electron jumps from the negative to the positive terminal?