(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

3m A. Find the unit vector that makes an angle (0 = - with the positive x-axis.

A hiker start from his parked car and walked as follows : 12km due east followed by 8km at 40 north of east , followed by 10km due . Find the components ( along east and north of the net displacement and the magnitude and direction of the displacement

Find the sum of the following vectors: and =< ♦

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. (Let  T2  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.) T2  =          |T2|  =  339.0511648       N T3  =          |T3|  =  276.5671494

Two athletes are pulling on a ring. One athlete pulls with a force of 239N in a northerly direction. The second athlete pulls with a force of 164N in a westerly direction. Calculate the magnitude and direction (relative to west) of the resultant of these two forces

If v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.

On the graph to the right, draw a coordinate axis. Draw in the two force vectors. Show by adding the vectors graphically that the net force on the central ring is zero. Verify this algebraically by showing that the sum of the. components is also zero. L +) = N the position. Now, notice that you can slide the ring back and forth along the r axis, placing it at any distance, and the ring will stay in place. This means that every point along the r axis is an equilibrium point. Explain why this is the case. The forces Cancel it does not matter FYEN Now we're going to change the axes. Remove the two pulleys, and place them at angles of 90° and 270°, respectively. Keeping the z axis along = 0, we've now placed the forces along the y axis. Repeat the earlier analysis with the new forces. 1D Trial 2 Results Force Magnitude (N) Direction (6) 0297 F₁ F₂ 0.48A/ 1 80 13 JEN Vector 0.294160 GrMB.NK 1800 F 11800

(1) A vertical force P = 150 lb is applied to the handle of the toggle clamp at A as shown. Determine clamping force under roller E and the magnitude of each connection force at pins B and D. Ans: E 1600 lb, B = 1415 lb, D = 1500 lb A 20" 8" D B 6" 8" E 6" ✓ F T 14"

(4) The two structural members, one of which is in 3 kN tension and the other in compression, exert the indicated forces on joint O. Determine the magnitude of the resultant R of the two forces and the angle 0 which the resultant vector makes with the +x-axis. Ans: R = 3.80 kN, 0=-21.6° (or 338°) 3 30° 2 kN