2. F ˆ F www.schoolDD.com 1
8
F
8.1. F F 1
F F ( F )
- F F F F
- F F F
- F F F F F
F F F F
8.2.
F F F
1. F F ˈ F
- F v --> a = 0 ∑ F = ma = 0
- F ω --> α = 0 ߬ = Iα = 0
2. F ˈ F
8.3. F F
F M ˈ F
F ˈ (N m)
∑ ۴റ = 0
∑ ۴ܠ = 0 = F
∑ ۴ܡ = 0 =
∑ ۻሬሬሬറ = 0 ∑ ۻ = ∑ ۻ
F
F
ℓ
O
ℓ
O
F
O +
ℓ
MO = Fर
3. F ˆ F www.schoolDD.com 2
2 F F F v
F F
1. F F F F F
2. F ( F ) F F , ∑ F = 0
3 F F F ˈ
1. F F
2. F F F , ∑ F = 0
3. F F F F , ∑ M = 0
mg
mg
T1
T2
θ
ba
CBA
F1
F3F2
mg sinθ
F
T
mg
N
m
F1F2
m
m
m
θ
F
∑ F୷ = 0
N = mg
∑ F୶ = 0
F1 = F2
∑ F୷ = 0
T = mg
∑ F = 0
F = mg sinθ
θ
α
F1
F3
F2
m
∑ F୷ = 0
F1 = F2 + F3
∑ M = 0
F1(a) = F3(a+b)
∑ M = 0
F2(a) = F3(b)
∑ Mେ = 0
F2(a+b) = F1(a)
∑ F୶ = 0
F1 = F2 cosθ + F3 cosα
∑ F୷ = 0
F2 sinθ = F3 sinα
∑ F୶ = 0
T2 cosθ = T1
∑ F୷ = 0
T2 sinθ = mg
4. F ˆ F www.schoolDD.com 3
8.4. F F
F F F F F
F F F
F 1
F 10 kg 2 m F F 2 F 20 kg F F
F F 0.40 m F F F ˈ F
F B ˈ
∑ M = ∑ M
mg(1.6) + W(1.0) = T1(2.0)
20(10)(1.6) + 100(1.0) = 2T1
T1 = 210 N Ans
∑ F୷ = 0
T1 + T2 = mg + W =
210 + T2 = 20(10) + 100
T2 = 90 N Ans
BA
1.00.4
2.0
T2
W
FF
ℓ
F
F
F
ℓ
F
ℓ
MC = Fर
T1
mg
m
5. F ˆ F www.schoolDD.com 4
F 2
10 kg 5 m 53 F .
F ˈ 0.4 F 50 kg ʾ F F F F
F ʾ F x F A F F F
fA
∑ F୷ = 0
NA = mg + W =
= 50(10) + 100
NA = 600 N
fA = µ NA
= 0.4(600)
fA = 240 N
∑ F୶ = 0
fA = NB = F
NB = 240 N
F A ˈ F
∑ M = ∑ M
NB(4.0) = W(1.5) + mg(x)
240(4.0) = 100(1.5) + 50(10)(x)
x = 1.62
୦
୶
= tan53
h = x tan53 = 1.62(4/3)
h = 2.16 m Ans
F
4.0
1.5
fA
NA
B
A
x
53°
5.0
h
W
NB
mg
53°
5.0
F
F
6. F ˆ F www.schoolDD.com 5
F 3
F 20 kg F
F B ˈ F F B
∑ M = ∑ M
Tsinθ(AB) = mg sinθሺ
ଶ
ሻ
T = ୫
ଶ
= ଶሺଵሻ
ଶ
T = 100 N Ans
F 4
16 kg F 10 kg F F F
F
F A ˈ F F F
∑ M = ∑ M
Tsin37(AB) = mg(AB) + Wሺ
ଶ
ሻ
T(ଷ
ହ
) = 10(10) + 160ሺ
ଵ
ଶ
ሻ
T = 300 N Ans
∑ F୶ = 0
Nx = T cos37 = F
T
N
Nx
Ny
mg
T cos37
T sin37T
W
mg
T cosθ
T sinθ
mg sinθ
mg cosθ
θ
A
B
ℓ
ℓ
θ A
B
θ
A B37°
m
A B37°
m
F
F
F
F
7. F ˆ F www.schoolDD.com 6
= 300(4/5)
Nx = 240 N
∑ F୷ = 0
Ny + T sin37 = mg + W =
Ny + 300 (3/5) = 10(10) + 160
Ny = 80 N
N = ටN୶
ଶ
N୷
ଶ
= √240ଶ 80ଶ
N = 80√10 N Ans
F 5
F F F 60 kg 0.50 m 0.20 m F
F F F F F F
F O ˈ
∑ M = ∑ M
F(0.3) = mg(0.4)
F = mg(0.4)/0.3 = 60(10)(0.4/0.3)
F = 800 N Ans
F 6
F F 1 m 2 m 15 kg F ˀ F . 0.5 F = 60 N
F 1.5 m F F F
N
1.0
2.0
O
N
mg
0.2
F 0.5
0.2
F
0.3
0.4
F
F
f
F
1.5
1.0
2.0
F
1.5
mg
F
F
8. F ˆ F www.schoolDD.com 7
F F F F
∑ F୶ = 0
f = F = F
µN = F
0.5(15)(10) = F
F = 75 N
F F F F 75 N F F
F F F F F F F ˈ
∑ M = ∑ M
F(1.5) = mg(1/2)
F = mg(1/2)/1.5 = 15(10)(1/2)/1.5
F = 50 N
F F F F 50 N F F F
F = 60 N F F F F Ans
F 7
F F F F . F F
ˈ 0.75 F F F ˈ F ˈ F F F
θ F F F
∑ F = 0
f = mg sinθ
µN = mg sinθ
0.75 mg cosθ = mg sinθ
0.75 = tanθ , θ = 37°
F θ = 37° Ans
θ F F F F F F F ˈ
N
mg sinθ
a
f mg
a
mg cosθ
θ θ
F
F
9. F ˆ F www.schoolDD.com 8
∑ M = ∑ M
mg sinθ (a/2) = mg cosθ (a/2)
tanθ = 1.0 , θ = 45°
F F θ = 45° Ans
8.5
F F
F F ˈ 3
1.
ˈ F F F F F
. F F cm. N mg F F F
F F
2. F
ˈ F F F F F F F
. cm. F F F F
3.
ˈ F F
. cm. F F N mg ˈ F F F F
8.6 F
F F F F F
F F F F ˈ F
mg
NN
mg
N mg
. . F .
10. F ˆ F www.schoolDD.com 9
F 8
F F F F F F F F F F ˈ
150 N
F F
∑ M = ∑ M
W (0.02) = F (0.15)
150 (0.02) = F (0.15)
F = 20 N Ans
F F 20 N F F 150 N
¬ F F F F F F F
F 9
F 120 kg F F F 2 m F F 240
F F F F ˈ F F
F
F F
∑ M = ∑ M
mg (x) = F (2-x)
120(10) x = 240 (2-x)
x = 0.33 m Ans
2 - x
mg
x F
0.150.02
R
W
F
F
F
0.150.02
F
F 1 F
11. F ˆ F www.schoolDD.com 10
F 10
F F ˈ F F F 40 kg
8.7 F
ˈ F
F F F F F F F
F F F F
F
1. F OA ˈ F F F ן ∆L ˈ A ˈ F F
F ן ∆L A F F F A F F
∆L F
2. F AB F F F F F F F F
F B F F F F B F F
L0 ΔL
C
D
O
A
B
F
F
mg
F
m
r = 0.2
R= 1.0
F F
∑ M = ∑ M
mg (0.2) = F (1.0)
40(10)(0.2) = F (1.0)
F = 80 N Ans
ΔL
L
F
12. F ˆ F www.schoolDD.com 11
3. F B ˈ F F F F F F
C ( ) ˈ F F F
F D F F
- F OB F F F F F
F
- F BD F F F
8.7.1. F
1. ˈ F F
2. ˈ F F
3. ˈ F F F
( F )
8.7.2. F
F (stress ) ߪ F F F F
ˈ F F ˈ F ( N/m2
)
( strain ) ߝ F F
ˈ F F
F F
ΔL
ΔL
A
F
FF F F F
F F
F
F F
F
A ߪ =
۴
ۯ
F F
L0
ࢿ =
ઢۺ
ۺ
13. F ˆ F www.schoolDD.com 12
8.7.3.
E ˈ F F F F ˈ F
(N/m2
)
- F E F
F 11
200 N F F F F 10 mm 1.0 m F 1.02 m
F F F
. F F A =
గ
ସ
d2
= 3.14(0.01)2
= 3.14x10-4
F ߪ =
=
ଶ
ଷ.ଵସ୶ଵష
= 6.37x105
N/m2
Ans
ߝ =
బ
=
.ଶ
ଵ.
= 0.02 Ans
F E =
ఙ
ఌ
=
.ଷ୶ଵఱ
.ଶ
= 3.18x107
N/m2
Ans
F 12
50 kg 2 m F 0.40 mm2
F ˈ 2x1010
ˈ F
E =
࣌
ࢿ
T
mg
m
L =1.02
ΔL =0.02
F =200 F = 200
L0 =1.0
14. F ˆ F www.schoolDD.com 13
T = mg = 50(10) = 500 N
ߪ =
=
=
ହ
.ସ୶ଵష
= 1.25x109
N/m2
ߝ =
బ
=
ΔL
ଶ.
E =
ఙ
ఌ
=
1.25x10
వ
୶ଶ.
ΔL
= 2.0x1010
N/m2
ΔL = 0.125 m
L = L0 + ΔL = 0.125 + 2.0
L = 2.125 m Ans
F 13
F F F (ߪ) (ߝ ) ˈ F
(E )
E =
ఙ
ఌ
=
E = ଶ୶ଵళ
ସ୶ଵషయ = 5.0x1010
N/m2
Ans
ߪ ( x107
N/m2
)
ߝ ( x10-3
)
20
10
420
