ENGR0135 - Statics and Mechanics of Materials 1 Homework #7

1. Locate the centroid of the shaded area shown below.

x

y3 in 3 in2 in

8 in

3 in

2. Locate the centroid of the slender rod shown below.

x

y50mm50mm

50mm

50mm

150mm

3. Locate the centroid of the shaded area shown below.

x

y

8 in

8 in

10 in 10 in

12 in

4. A cylinder with a hemispherical cap is shown below. The radius of the cylinder and ofthe hemispherical cap is R = 150mm and the height of the cylinder is h = 200mm

(a) Locate the centroid of the composites volume.

(b) Locate the center of gravity of the composite volume if the cylinder is made ofsteel (ρ = 7870 kg/m3) and the hemisphere is made of titanium (ρ = 4630 kg/m3).

x

y

z

R

R

h

5. A distributed load acts on a beam as shown below. Determine the resultant of thedistributed load and locate its line of action with respect to the support at A.

x

y

3 kN/m

7 kN/m

2m 4m

A B

6. Draw a free-body diagram of the angle bracket shown below. The angle bracket issupported by a roller at B and a smooth pin at C.

AB

C

P

7. Draw a free-body diagram of the box shown below. The box has weight W and isresting on a rough surface.

P

G

20◦

25◦

8. Draw a free-body diagram of the door shown below. The homogeneous door has weightW and the pair of hinges A and B are properly aligned. The force T is due to thetension in cable CD.

x

y

z

A B

C

D

T