Chapter 12

$x=1.3\text{m}$

(b), (c)

316.7 g; 5.8 N

$T=\text{1963 N};\text{F}=1732\text{N}$

${\mu }_s<0.5\text{cot}\beta$

${\overrightarrow{F}}_{\text{door on}A}=100.0\text{N}\widehat{i}-200.0\text{N}\widehat{j}\text{;}{\overrightarrow{F}}_{\text{door on}B}=\mathrm{-100.0}\text{N}\widehat{i}-200.0\text{N}\widehat{j}$

711.0 N; 466.0 N

1167 N; 980 N directed upward at $18\text{°}$ above the horizontal

$206.8\text{kPa};4.6\times {10}^{\mathrm{-5}}$

$5.0\times {10}^{\mathrm{-4}}$

63 mL

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

constant

magnitude and direction of the force, and its lever arm

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

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

It helps a wire-walker to maintain equilibrium.

(Proof)

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

tightly

compressive; tensile

no

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

$46.8\text{N}·\text{m}$

4,472 N, 153.4°

23.3 N

80.0 kg

40 kg

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

784 N, 132.8 N

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

tension 778 N; at hinge 778 N at $45\text{°}$ above the horizontal; no

1500 N; 1620 N at $30\text{°}$

1.2 mm

32.9 cm

$4.0\times {10}^2{\text{N/cm}}^2$

$11.9\text{μm}$

0.57 mm

8.59 mm

$1.35\times {10}^9\text{Pa}$

259.0 N

0.01%

1.44 cm

0.63 cm

${\text{tan}}^{\mathrm{-1}}(1\text{/}{\mu }_s)=51.3\text{°}$

a. at corner 66.7 N at $30\text{°}$ with the horizontal; at floor 177 N at $109\text{°}$ with the horizontal; b. ${\mu }_{\text{s}}=0.346$

a. $1.10\times {10}^9{\text{N/m}}^2;$ b. $5.5\times {10}^{\mathrm{-3}};$ c. 11.0 mm, 31.4 mm

$F=\mathit{\text{Mg}}\text{tan}\theta ;f=0$

with the horizontal, $\theta =42.2\text{°};$ $\alpha =17.8\text{°}$ with the steeper side of the wedge

$W(l_1\text{/}{l}_2-1);W{l}_1\text{/}{l}_2+mg$

a. 1.1 mm; b. 6.6 mm to the right; c. $1.11\times {10}^5\text{N}$