(1) A square foundation mat supports the four columns and each column carries a vertical load shown. Determine the location on the mat of the point of application of the single resultant force of the four loads. Ans: x = 3.5 ft, z=3 ft 20 kips 40 kips 6 ft B 8 kips 12 kips 5 ft

A wrench 25 cm long lies along the positive y-axis and grips a bolt at the origin. A force is applied in the direction (a.3.-4) at the end of the wrench. Find the magnitude of the force needed to supply 100 N · m of torque to the bolt. (Round your answer to the nearest whole number.)

A block-and-tackle pulley hoist is suspended in a warehouse by ropes of lengths 2 m and 3 m. The hoist weighs 430 N. The ropes, fastened at different heights, make angles of 50° and 38° with the horizontal. Find the tension in each rope and the magnitude of each tension (in N). (Let T, and T3, represent the tension vectors corresponding to the ropes of length 2 m and 3 m respectively. Round all numerical values to two decimal places.) 38° 50° 3 m 2 m T2 X N |T2l X N T3 X N = |T3| = X N

Two construction workers are lifting a beam using ropes. Worker A pulls with a force of 500 newtons at an angle of 40°with the positive x-axis. Worker B is on the opposite side pulling with a force of 380 newtons at an angle of 115 ° with the positive x- axis. Find the (a) magnitude and (b) direction angle of the resultant force. (Round to the nearest hundredths)