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Burka [1]
3 years ago
7

Many caterpillars construct cocoons from silk, one of the strongest naturally occurring materials known. Each thread is typicall

y 2.0 μm in diameter and the silk has a Young's modulus of
4.0 ✕ 109 N/m2.

(a) How many strands would be needed to make a rope 11 m long that would stretch only 1.00 cm when supporting a pair of 85-kgmountain climbers?
✕ 106 strands

(b) Assuming that there is no appreciable space between the parallel strands, what would be the diameter of the rope?
Physics
2 answers:
joja [24]3 years ago
6 0

Answer:

a) N = 145,833,674.52174 = 1.458 × 10⁸ strands

b) diameter of single rope with the same effect = 2.415 cm

Explanation:

Hooke's law explains that stress is directly proportional to strain.

Stress ∝ Strain.

Stress = E × Strain

E = constant of proportionality = Young's Modulus = 4.0 ✕ 10⁹ N/m².

Stress = (Load/Total Cross sectional Area)

Load = a pair of 85 kg mountain climbers = 85 × 2 × 9.8 = 1666 N

Total Cross sectional Area = (Number of strands) × (Area of one strand) = A

Strain = (ΔL/L)

ΔL = 1.00 cm = 0.01 m

L = 11 m

Strain = (0.01/11) = 0.0009091

Stress = (Young's Modulus) × (Strain) = (4.0 ✕ 10⁹) × (0.0009091) = 3,636,363.64 N/m²

(Load/ total Area) = 3,636,363.64

Total area = (Load/3,636,363.64) = (1666/3,636,363.64) = 0.00045815 m²

Recall,

Total Cross sectional Area = (Number of strands) × (Area of one strand)

Area of one strand = (πd²/4)

diameter of one strand = 2 μm = (2×10⁻⁶) m

Area of one strand = (πd²/4)

= π × (2×10⁻⁶)² ÷ 4 = (3.142 × 10⁻¹²) m²

Total Cross sectional Area = (Number of strands) × (Area of one strand)

0.00045815 = N × (3.142 × 10⁻¹²)

N = 145,833,674.52174 = 1.458 × 10⁸ strands

b) If it was a single rope, the cross sectional Area would just be equal to the total cross sectional Area obtained in (a)

A = 0.00045815 m²

A = (πD²/4)

where D = diameter of the single rope

0.00045815 = (πD²/4)

D² = (4×0.00045815) ÷ π = 0.0005833347

D = 0.02415 m = 2.415 cm

Hope this Helps!!!

GrogVix [38]3 years ago
4 0

Answer:

Explanation:

Young modulus of the silk E = stress / strain = \frac{F}{A} / \frac{DL}{L} = \frac{FL}{ADL}

A = \frac{FL}{EDL} where F = weight of the pair = 2 × 85 × 9.8 = 1666N, L, length = 11 m and DL, extension = 1.0cm = 0.01 m

A = \frac{1666* 11 }{4.0 * 109 * 0.01 } = 0.00045815 M²

Area of the silk = πr²,  r = diameter / 2 =2/2 = 1 × 10⁻⁶ m ( 1μm = 10⁻⁶ m)

Area of silk = 3.142 ×( 1 × 10⁻⁶ m)² = 3.142 × 10⁻¹²

number of strands = 0.00045815 m² / 3.142 × 10⁻ ¹² = 145814767.7 strands

b) the diameter of the rope = 145814767.7 × 2 × 10⁻⁶ = 291.63 m

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Maksim231197 [3]

Answer:

7.00 m

Explanation:

Given:

v₀ = 2.00 m/s

v = 5.00 m/s

a = 1.50 m/s²

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v² = v₀² + 2aΔx

(5.00 m/s)² = (2.00 m/s)² + 2(1.50 m/s²)Δx

Δx = 7.00 m

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3 years ago
Earth's gravitational field is strongest at _______.
Serga [27]
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2 years ago
A spring of force constant 1500 Nm-l is acted
olchik [2.2K]

Answer:

1.876 J

Explanation:

First, let’s calculate the compression of the spring from the Hooke’s law:

F=kx,

here, F=75 N is the force acted on the spring, k=1500 N⁄m is the force constant of the spring, x is the compression of the spring.

Then, we get:

x=F/k=(75 N)/(1500 N/m)=0.05 m.

Finally, we can find the potential energy stored in the spring:

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7 0
3 years ago
The mass of M1 = 12 Daltons and it has a speed of v1 = 200 m/s. The mass of M2 = 4 Daltons. What was the total momentum of the s
svet-max [94.6K]

Answer:

The total momentum is  p__{T }} =(2400  -4 v_2) \ Dalton \cdot m/s

Explanation:

The diagram illustration this  system is shown on the first uploaded image (From physics animation)

From the question we are told that

     The mass of the first object is M_1 =  12 \ Dalton

      The speed of the first mass is v_1 =  200 \ m/s

      The mass of the second object is  M_2 =  4 \ Dalton

      The speed of the second object is  assumed to be  - v_2

The total momentum of the system is the combined momentum of both object which is mathematically represented as

           p__{T }} = M_1 v_1 + M_2 v_2

   substituting values

            p__{T }} = 12 * 200 + 4 * (-v_2)

            p__{T }} =(2400  -4 v_2) \ Dalton \cdot m/s

7 0
3 years ago
During an auto accident, the vehicle's air bags deploy and slow down the passengers more gently than if they had hit the windshi
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Answer:

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Explanation:

t = Time taken = 36 ms

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration = 60g

g = Acceleration due to gravity = 9.81 m/s²

v=u+at\\\Rightarrow u=v-at\\\Rightarrow u=0-(-9.81\times 60)\times 36\times 10^{-3}\\\Rightarrow u=21.1896\ m/s

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The distance the person traveled is 0.3814128 m

4 0
3 years ago
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