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3 years ago

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A vertical solid steel post of diameter d = 26cmand length L = 2.40m is required to support a load of mass m = 7800kg . You can

ignore the weight of the post. Take free fall acceleration to be g=9.8m/s2.Part AWhat is the stress in the post?Express your answer using two significant figures.Part BWhat is the strain in the post?Express your answer using two significant figures.Part CWhat is the change in the post's length when the load is applied?Express your answer using two significant figures.

1 answer:

givi [52]3 years ago

7 0

Answer

given,

diameter of steel = d = 26 c m

radius = 13 cm = 0.13 m

length = L = 2.4 m

mass = 7800 Kg

g = 9.8 m/s²

a) stress = F/A

stress = $\dfrac{mg}{\pi\ r^2}$

stress = $\dfrac{7800 \times 9.8}{\pi\ 0.13^2}$

stress = 1.44 x 10⁶ N/m²

b) Young's modulus x strain = stress

Young's modulus for steel = 200 x 10⁹ N/m²

200 x 10⁹ x strain = 1.44 x 10⁶

strain = 7.2 x 10⁻⁶ m

c) change in length

$Strain= \dfrac{\Delta L}{L}$

$7.2 \times 10^{-6} = \dfrac{\Delta L}{2.4}$

$\Delta L= 17.28\times 10^{-6}\ m$

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Answer:

170 N

Explanation:

Since Force F = ma were m = mass = 85 kg and a = acceleration = 2.0 m/s².

So the net force on the bicycle is

F = ma = 85 kg × 2.0 m/s² = 170 N

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1. What is the intensity of a sound when an observer is 10.0 m from the speaker

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Answer:

About 133 db.

Explanation:

Sound Intensity Level in db (SIL db) is equal to 10log (base 10) times the ratio of the sound intensity at 200 watts (I) relative to the sound intensity of the reference sound intensity (I sub 0), which by default is equal to 10⁻¹² W/m² or 0 dB.

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Marta_Voda [28]

a) The momentum of the coconut is 3 kg m/s

b) At first, the air resistance is negligible, so the coconut accelerates due to the force of gravity

c) The coconut reaches its terminal velocity

Explanation:

a)

The momentum of an object is given by the equation

$p=mv$

where

m is the mass of the object

v is its velocity

For the coconut in this problem, we have:

m = 1.5 kg (mass)

v = 2 m/s (velocity)

Therefore, its momentum is

$p=(1.5)(2)=3 kg m/s$

B)

There are only two forces acting on the coconut during its fall:

The force of gravity, of magnitude $mg$ (m= mass of the coconut, g = acceleration of gravity), acting downward
The air resistance, acting upward, whose magnitude is proportional to the speed of the coconut

During the first momentums of the fall, the speed of the coconut is still low, so the air resistance is mostly negligible, and therefore only the force of gravity is acting on the coconut. Since this force is constant, it means that the acceleration of the coconut is constant: therefore, its velocity keeps increasing during the fall, and the coconut speeds up.

C)

If the tree is very tall, the fall of the coconut lasts long, and the speed of the coconut keeps increasing. Since the air resistance is proportional to the speed, this means that at some point, the air resistance is no longer negligible, and it starts to have some effect on the fall of the coconut. In particular, at a certain point, the air resistance will become equal (in magnitude) to the force of gravity (but opposite in direction): this means that from this point, the acceleration of the coconut will be zero, and therefore the coconut will continue its motion at constant velocity. This velocity is called terminal velocity, and it occurs when the force of gravity is equal to the air resistance:

$mg = F_r$

where $F_r$ is the air resistance.

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3 years ago

Hydrogen is in Group 1A of the periodic table, known as the alkali metals, although it obviously isn't a metal. What is the reas

jeka57 [31]

It's highly reactive and contains only one valence electron

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series RC circuit is built with a 15 kΩ resistor and a parallel-plate capacitor with 18-cm-diameter electrodes. A 18 V, 36 kHz s

andre [41]

Answer:

$d=1.84\ mm$

Explanation:

<u>Capacitance</u>

A two parallel-plate capacitor has a capacitance of

$\displaystyle C=\frac{\epsilon_o A}{d}$

where

$\epsilon_o=8.85\cdot 10^{-12}\ F/m$

A = area of the plates = $\pi r^2$

d = separation of the plates

$\displaystyle d=\frac{\epsilon_o A}{C}=\frac{\epsilon_o \pi r^2}{C}$

We need to compute C. We'll use the circuit parameters for that. The reactance of a capacitor is given by

$\displaystyle X_c=\frac{1}{wC}$

where w is the angular frequency

$w=2\pi f=2\pi \cdot 36000=226194.67\ rad/s$

Solving for C

$\displaystyle C=\frac{1}{wX_c}$

The reactance can be found knowing the total impedance of the circuit:

$Z^2=R^2+X_c^2$

Where R is the resistance, $R=15 K\Omega=15000\Omega$ . Solving for Xc

$X_c^2=Z^2-R^2$

The magnitude of the impedance is computed as the ratio of the rms voltage and rms current

$\displaystyle Z=\frac{V}{I}$

The rms current is the peak current Ip divided by $\sqrt{2}$ , thus

$\displaystyle Z=\frac{\sqrt{2}V}{I_p}$

$I_p=0.65\ mA/1000=0.00065\ A$

Now collect formulas

$\displaystyle X_c^2=Z^2-R^2=\left(\frac{\sqrt{2}V}{I_p}\right)^2-R^2$

Or, equivalently

$\displaystyle X_c=\sqrt{\frac{2V^2}{I_p^2}-R^2}$

$\displaystyle X_c=\sqrt{\frac{2\cdot 18^2}{0.00065^2}-15000^2}$

$X_c=36176.34\ \Omega$

The capacitance is now

$\displaystyle C=\frac{1}{226194.67\cdot 36176.34}=1.22\cdot 10^{-10}\ F$

The radius of the plates is

$r=18\ cm/2=9 \ cm = 0.09 \ m$

The separation between the plates is

$\displaystyle d=\frac{8.85\cdot 10^{-12} \cdot \pi\cdot 0.09^2}{1.22\cdot 10^{-10}}$

$d=0.00184\ m$

$\boxed{d=1.84\ mm}$

8 0

3 years ago