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Nezavi [6.7K]
3 years ago
8

The solid aluminum shaft has a diameter of 50 mm. Determine the absolute maximum shear stress in the shaft and sketch the shear-

stress distribution along a radial line of the shaft where the shear stress is maximum. Set T1
Engineering
1 answer:
jarptica [38.1K]3 years ago
5 0

Answer:

Max shear = 8.15 x 10^7 N/m2

Explanation:

In order to find the maximum stress for a solid shaft having radius r, we will be applying the Torsion formula which can be written as;

Allowable Shear Stress = Torque x Radius / pi/2 x radius^4

Putting the values we have;

T = 2000 N/m

Radius = Diameter/2 = 0.05 / 2 = 0.025 m

Putting values in formula;

Max shear = 2000 x 0.025 / 3.14/2 x (0.025)^4

Max shear = 8.15 x 10^7 N/m2

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Disk A has a mass of 8 kg and an initial angular velocity of 360 rpm clockwise; disk B has a mass of 3.5 kg and is initially at
garri49 [273]

Answer:

A. αa= 9.375 rad/s^2, αb= 28.57 rad/s^2

B. ωa=251rpm, ωb=333rpm

Explanation:

Mass of disk A, m1= 8kg

Mass of disk B, m2= 3.5kg

The initial angular velocity of disk A= 360rpm

The horizontal force applied = 20N

The coefficient of friction μk = 0.15

While slipping occurs, a frictional force is applied to disk A and disk B

T= 1/2Mar^2a

T=1/2 (8kg) (0.08)^2

T= 0.0256kg-m^2

N=P=20N

F= μN

F= 0.15 × 20

F=3N

We have

Summation Ma= Summation(Ma) eff

Fra= Iaαa

(3N)(0.08m)= (0.0256kg-m^2)α

αa= 9.375 rad/s^2

The angular acceleration at disk A is αa= 9.375 rad/s^2 is acting in the anti-clockwise direction.

For Disk B,

T= 1/2Mar^2a

T= 1/2(3.5) (0.06)^2

=0.0063kg-m^2

We have,

Summation Mb= Summation(Mb) eff

Frb= Ibαb

(3N)(0.06m)= (0.0063kg-m^2) α

αb= 28.57 rad/s^2

B) ( ωa)o= 360rpm(2 pi/60)

= 1 pi rad/s

The disk will stop sliding where

ωara=ωbrb

(ωao-at)ra=αtr

(12pi-9.375t) (0.08)=28.57t(0.06)

(37.704-9.375t)(0.08)= 1.7142t

3.01632-0.75t= 1.7142t

t=1.22s

Now,

ωa=(ωa)o- t

12pi - 9.375(1.22)

37.704-11.4375

=26.267 rad/s

26.267× (60/2pi)

= 250.80

251rpm

The angular velocity at a, ω= 251rpm

Now,

ωb= αbt

=28.57(1.22)

=34.856rad/s

34.856rad/s × (60/2pi)

=332.807

= 333rpm

Therefore the angular velocity at b ω=333rpm

4 0
3 years ago
Read 2 more answers
A 20 mm diameter rod made of ductile material with a yield strength of 350 MN/m2 is subjected to a torque of 100 N.m, and a bend
vodka [1.7K]

Answer:

a) 42.422 KN

b) 44.356 KN

Explanation:

Given data :

Diameter = 20 mm

yield strength = 350 MN/m^2

Torque ( T )  = 100 N.m

Bending moment = 150 N.m

<u>Determine the value of the applied axial tensile force when yielding of rod occurs </u>

first we will calculate the shear stress and normal stress

shear stress ( г ) = Tr / J = [( 100 * 10^3)  * 10 ]  /  \pi /32 * ( 20)^4  

                                       = 63.662 MPa

Normal stress(  Гb + Гa )  = MY/ I  +  P/A

= [( 150 * 10^3)  * 10 ]  /  \pi /32 * ( 20)^4   + 4P / \pi  * 20^2

= 190.9859 + 4P / \pi  * 20^2  MPa

<u>a) Using MSS theory </u>

value of axial force = 42.422 KN

solution attached below

<u>b) Using MDE  theory </u>

value of axial force = 44.356 KN

solution attached below

5 0
3 years ago
Assume the transistor is biased in the saturation region at VGS 4 V. (a) Calculate the ideal cutoff frequency. (b) Assume that t
insens350 [35]

Answer:

hello your question is incomplete attached below is the complete question and the detailed solution

Answer: A) 5.17 GHz

              B) 1.01 GHz

Explanation:

Assuming the transistor is biased and considering the two conditions as given in A and B attached below is a detailed solution to the given problem

4 0
3 years ago
The barrel of a bicycle tire pump becomes quite warm during use. Explain the mechanisms responsible for the temperature increase
Alexeev081 [22]

Answer:

The air heats up when being compressed and transefers heat to the barrel.

Explanation:

When a gas is compressed it raises in temperature. Assuming that the compression happens fast and is done before a significant amount of heat can be transferred to the barrel, we could say it is an adiabatic compression. This isn't exactly true, it is an approximation.

In an adiabatic transformation:

P^{1-k} * T^k = constant

For air k = 1.4

SO

P0^{-0.4} * T0^{1.4} = P1^{-0.4} * T1^{1.4}

T1^{1.4} = \frac{P1^{0.4} * T0^{1.4}}{P0^{0.4}}

T1^{1.4} = \frac{P1}{P0}^{0.4} * T0^{1.4}

T1 = T0 * \frac{P1}{P0}^{0.4/1.4}

T1 = T0 * \frac{P1}{P0}^{0.28}

SInce it is compressing, the fraction P1/P0 will always be greater than one, and raised to a positive fraction it will always yield a number greater than one, so the final temperature will be greater than the initial temperature.

After it was compressed the hot air will exchange heat with the barrel heating it up.

5 0
3 years ago
In order to impress your neighbors and improve your vision in traffic jams, you decide to mount a cylindrical periscope 2.0 m hi
kondaur [170]
Follow @richard.gbe on Instagram for the answer
5 0
4 years ago
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