ENGR0135 - Statics and Mechanics of Materials 1 (2211)Homework #6

1. Replace the 40 lb force exerted on the wrench shown below with an equivalent force-couple system at the nut A.

40 lb

5 in

A

2. Determine the resultant of the four forces acting on the truss shown below and deter-mine where the resultant intersects the x-axis.

2m 2m

2m

2m

2mA B x

y

10 kN

60◦

2 kN

2 kN

2 kN

3. Four parallel forces act on a concrete slab, as shown below. Determine the resultantof the forces and locate the intersection of the line of action of the resultant with thexy-plane.

x

y

z

10 in 10 in 10 in 10 in

16 in

16 in

100 lb

100 lb

150 lb

200 lb

4. The homogeneous plate shown below weighs 240 lb. The magnitude of the force T incable CD is 200 lb. Replace the weight and cable forces by an equivalent force-couplesystem at hinge A.

10 in

21 in63 in

64 in

59 in

42 in

50 in

x

y

z

A B

C

D

T

5. Three particles with masses of 20, 30, and 100 kg are located at points with (x, y, z)coordinates of (−5,−5, 10), (−5,−5, 5), and (0, 2, 0), respectively, where distances aremeasured in meters. Determine the coordinates of the center of mass for the threeparticles.

6. Determine the x- and y-coordinates of the centroid of the shaded area shown below.

x

y

y =x2

2b

b

2

b