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Natasha_Volkova [10]

3 years ago

13

A disk between vertebrae in the spine is subjected to a shearing force of 425 N. Find its shear deformation, taking it to have a

shear modulus of 1.70×10^9 N/m^2. The disk is equivalent to a solid cylinder 0.700 cm high and 6.50 cm in diameter. a) 5.27 x 10^-7 m
b) 1.54 x 10^-6 m
c) 3.08 x 10^-6 m
d) 6.16 x 10^-6 m

1 answer:

zzz [600]3 years ago

3 0

Answer:

option A

Explanation:

given,

shear force = 425 N

Shear modulus = 1.7 × 10⁹ N/m²

disk equivalent to solid cylinder

height = 0.7 cm and diameter = 6.50 cm

$\delta = \dfrac{VL}{AG}\\\\\delta = \dfrac{425\times 0.007}{0.25 \times \pi d^2\times 1.7\times 10^9}\\\\\delta = \dfrac{425\times 0.007}{0.25 \times \pi\times 0.065^2\times 1.7\times 10^9}\\\\\delta = 5.27 \times 10^{-7} m$

hence, the correct answer is option A

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Zigmanuir [339]

Answer:

The tension in each half of the rope, is approximately 4,908.8 N

Explanation:

The mass of the acrobat, m = 60 kg

The length of the rope, l = 10 m

The extent by which the center dropped = 30 cm = 0.3 m

Let, 'T' represent the tension in each half of the rope

Weight, W = Mass, m × The acceleration due to gravity, g

∴ W = m × g

The acceleration due to gravity, g ≈ 9.8 m/s²

∴ The weight of the acrobat, W = 60 kg × 9.8 m/s² ≈ 588 N

The angle the dropped rope makes with the horizontal, θ is given as follows;

θ = arctan((0.3 m)/(5 m)) = arctan(0.06) ≈ 3.434°

At equilibrium, the sum of vertical forces, $\Sigma F_y$ = 0

The vertical component of the tension, $T_y$ , in each half of the rope is given as follows;

$T_y$ = T × sin(θ)

∴ $\Sigma F_y$ = W + T × sin(θ) + T × sin(θ) = W + 2 × T × sin(θ)

Plugging in the values, with θ = arctan(0.06) for accuracy, we get;

588 N + 2 × T × sin(arctan(0.06) = 0

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So, the velocity can be obtained by integrating this expression:

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The velocity is, by definition: $v=\frac{dx}{dt}$ , so

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Answer:

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