 University Physics Volume 1

# Chapter 12

12.1

$x = 1.3 m x = 1.3 m$

12.2

(b), (c)

12.3

316.7 g; 5.8 N

12.4

$T = 1963 N ; F = 1732 N T = 1963 N ; F = 1732 N$

12.5

$μ s < 0.5 cot β μ s < 0.5 cot β$

12.6

$F → door on A = 100.0 N i ^ − 200.0 N j ^ ; F → door on B = −100.0 N i ^ − 200.0 N j ^ F → door on A = 100.0 N i ^ − 200.0 N j ^ ; F → door on B = −100.0 N i ^ − 200.0 N j ^$

12.7

711.0 N; 466.0 N

12.8

1167 N; 980 N directed upward at $18°18°$ above the horizontal

12.9

$206.8 kPa ; 4.6 × 10 −5 206.8 kPa ; 4.6 × 10 −5$

12.10

$5.0 × 10 −4 5.0 × 10 −4$

12.11

63 mL

12.12

Fluids have different mechanical properties than those of solids; fluids flow.

### Conceptual Questions

1 .

constant

3 .

magnitude and direction of the force, and its lever arm

5 .

True, as the sum of forces cannot be zero in this case unless the force itself is zero.

7 .

False, provided forces add to zero as vectors then equilibrium can be achieved.

9 .

It helps a wire-walker to maintain equilibrium.

11 .

(Proof)

13 .

In contact with the ground, stress in squirrel’s limbs is smaller than stress in human’s limbs.

15 .

tightly

17 .

compressive; tensile

19 .

no

23 .

It acts as “reinforcement,” increasing a range of strain values before the structure reaches its breaking point.

### Problems

25 .

$46.8 N · m 46.8 N · m$

27 .

4,472 N, 153.4°

29 .

23.3 N

31 .

80.0 kg

33 .

40 kg

35 .

right cable, 444.3 N; left cable, 888.5 N; weight of equipment 156.8 N; 16.0 kg

37 .

784 N, 132.8 N

39 .

a. 539 N; b. 461 N; c. do not depend on the angle

41 .

tension 778 N; at hinge 778 N at $45°45°$ above the horizontal; no

43 .

1500 N; 1620 N at $30°30°$

45 .

1.2 mm

47 .

32.9 cm

49 .

$4.0×102N/cm24.0×102N/cm2$

51 .

$0.149 μm 0.149 μm$

53 .

0.57 mm

55 .

8.59 mm

57 .

$1.35 × 10 9 Pa 1.35 × 10 9 Pa$

59 .

259.0 N

61 .

0.01%

63 .

1.44 cm

65 .

0.63 cm

69 .

$tan −1 ( 1 / μ s ) = 51.3 ° tan −1 ( 1 / μ s ) = 51.3 °$

71 .

a. at corner 66.7 N at $30°30°$ with the horizontal; at floor 177 N at $109°109°$ with the horizontal; b. $μs=0.346μs=0.346$

73 .

a. $1.10×109N/m2;1.10×109N/m2;$ b. $5.5×10−3;5.5×10−3;$ c. 11.0 mm, 31.4 mm

### Challenge Problems

75 .

$F = Mg tan θ ; f = 0 F = Mg tan θ ; f = 0$

77 .

with the horizontal, $θ=42.2°;θ=42.2°;$ $α=17.8°α=17.8°$ with the steeper side of the wedge

79 .

$W ( l 1 / l 2 − 1 ) ; W l 1 / l 2 + m g W ( l 1 / l 2 − 1 ) ; W l 1 / l 2 + m g$

81 .

a. 1.1 mm; b. 6.6 mm to the right; c. $1.11×105N1.11×105N$

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