ENGR0135 - Statics and Mechanics of Materials 1 Homework #7 1. Locate the centroid of the shaded area shown below. x y 3 in 3 in 2 in 8 in 3 in 2. Locate the centroid of the slender rod shown below. x y 50 mm 50 mm 50 mm 50 mm 150 mm 3. Locate the centroid of the shaded area shown below. x y 8 in 8 in 10 in 10 in 12 in
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ENGR0135 Statics and Mechanics of Materials 1 Homework #7pitt.edu/~qiw4/Academic/ENGR0135/HW7.pdfthe hemispherical cap is R= 150mm and the height of the cylinder is h= 200mm (a) Locate
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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.