As shown, a 2.7-lblb ball is suspended at point D inside a box with dimensions w=8.90 ft, ft, d=6.50ft . The ball is held in place by three cables anchored at points A, B, and C on the surface of the box. point D is the origin of the Cartesian coordinate system, point A is located at (−4.60,−3.60,2.80)ft, point B is located at (1.90,−3.60,1.90) ft, and point C is located at (1.90,5.30,−1.70) ft. 1.The tension in cable DA has a magnitude of TDA lb. Find the Cartesian components of tension TDA , which is directed from D to A. 2.If the tensions in cables DA and DB are TDA =7.23 lb and TDB =5.20 lb, respectively, what is the tension in cable DC?

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5. Consider the flat object bounded by the curves y = 4x and y = Vx +b where (b=2). The area density of the M object is o = yx where the relationship between the total mass M and y is = 0.0309. Find the y-coordinate of the center of mass of this object (do not find the x coordinate of the center of mass). 1 y em Ym = vdm M

The traffic light shown below is supported by a system of cables. Points A and B are in a vertical plane which is parallel to the x-z plane. Point C is in the y-z plane. B Z X The traffic light has a mass of 75 kg The distances are: a = 4m, b = 6 m, c = 9 m, h = 6 m To answer the next set of questions you will determine the following: a. Position vectors for OA, OB, OC b. Unit vectors for OA, OB, OC c. Overall equilibrium equation d. Equilibrium equations in each of the x, y and z directions e. The tensions in the cables OA, OB and OC The traffic light has a mass of 75 kg. The distances are: a = 4 m, b = 6 m, c = 9 m, h = 6 m. Determine the position vector for OA. The position vector FOA can be written in the form: TOA = TOAzi+TOAİ+TOA-k You will have to input each of these three components separately below. Given: • The x component of the position vector,IOA = 4 m. • They component of the position vector,TOA = -9 m. 1. What is the z component of the position vector,TOA? Please report…