(3) Two vertical forces are applied as shown to boom AB which is supported by a ball-and-socket joint at A and cables BC and DE. The weight of the boom is negligible and cable DE is horizontal along the x-axis. Determine the tension forces T1 and T2 in the cables. Ans: T₁ 91.5 kN, T₂ = 53.3 kN 4 m 3 m 4 m T2. D T₁₂ H/2m 3 m 20 kN 30 kN

(5) A force T is applied at the tip of the rod as shown. If the n- component of the force is T, = 35 lb, determine the t-, x-, and y-components of the force T. The t-axis is directed along the rod, and the n-axis is perpendicular to the rod. Ans: T₁ =-130.6 lb, Tx=-103.6 lb, Ty = -86.9 lb T n 40° O 55°

(3) Compute the couple by the two parallel forces shown for F = 65 lb. Ans: M=2300 lb-ft CCW 20% F y, ft A (-10, 14) C (-12, -12) D (20, 0) x, ft B (20,-7) F 20°

A basket of flowers of mass 3 kg is placed on a flat grassy slope that makes an angle θ with the horizontal. The coefficient of static friction between the basket and the slope is 0.45 and the basket is on the point of slipping down the slope. Model the basket of flowers as a particle and the grassy slope as a plane. Take the magnitude of the acceleration due to gravity, g, to be 9.8 m s−2 Express the forces in component form, in terms of θ and unknown magnitudes where appropriate. Write down the equilibrium condition for the basket and hence show that tan θ = 0.45. Determine the angle, in degrees, that the slope makes with the horizontal.

(5) For the two-bar frame shown, determine the magnitudes of the connection force at pin B and the reaction at pin C for a weight of W= 2400 lb. Ans: B 9330 lb, C= 8350 lb W 5' B 5' D 3'

(6) A force of 200 N is applied perpendicular to the wrench at its tip as shown. Determine the equivalent force-couple system at center O of the wheel. Ans: F=68.4-187.9 N, Mo = 78.3 N'm CW 650 mm 125 mm 450 mm 20° 200 N

(4) A force F is applied through the bar on the slider at A as shown. If the t-component of the force is Ft = 90 N, determine the n-, x-, and y-components of the force F. Ans: Fn=-107.3 N, Fx = 131.6 N, Fy = -47.9 N F 20° n 30°

(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"

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