A prismatic bar AB of length L and solid circular cross section (diameter d) is loaded by a distributed torque of constant intensity t per unit distance .
(a) Determine the maximum shear stress tmax in the bar
(b) Determine the angle of twist between the ends of the bar.

Answers

Answer 1

Answer:

a) the maximum shear stress τ\(_{max}\) the bar is 16T\(_{max}\) /πd³

b) the angle of twist between the ends of the bar is 16tL² / πGd⁴  

Explanation:

Given the data in the question, as illustrated in the image below;

d is the diameter of the prismatic bar of length AB

t is the intensity of distributed torque

(a) Determine the maximum shear stress tmax in the bar

Maximum Applied torque  T_max = tL

we know that;

shear stress τ = 16T/πd³

where d is the diameter

so

τ\(_{max}\) = 16T\(_{max}\) /πd³

Therefore, the maximum shear stress τ\(_{max}\) the bar is 16T\(_{max}\) /πd³

(b) Determine the angle of twist between the ends of the bar.

let theta (\(\theta\)) be the angle of twist

polar moment of inertia \(I_p}\) = πd⁴/32

now from the second image;

lets length dx which is at distance of "x" from "B"

Torque distance x

T(x) = tx

Elemental angle twist = d\(\theta\) = T(x)dx / G\(I_{p}\)

so

d\(\theta\) = tx.dx / G(πd⁴/32)

d\(\theta\) = 32tx.dx / πGd⁴

so total angle of twist \(\theta\) will be;

\(\theta\) =  \(\int\limits^L_0 \, d\theta\)

\(\theta\) =  \(\int\limits^L_0 \,\) 32tx.dx / πGd⁴

\(\theta\) = 32t / πGd⁴  \(\int\limits^L_0 \, xdx\)

\(\theta\) = 32t / πGd⁴ [ L²/2]

\(\theta\) = 16tL² / πGd⁴  

Therefore,  the angle of twist between the ends of the bar is 16tL² / πGd⁴  

A Prismatic Bar AB Of Length L And Solid Circular Cross Section (diameter D) Is Loaded By A Distributed
A Prismatic Bar AB Of Length L And Solid Circular Cross Section (diameter D) Is Loaded By A Distributed

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Answers

Answer:

B = 2.19*10^-7 T

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Solution -

As per the given-

Mass of runner m = 74kg

initial velocity of runner u=4.8 m/s

final velocity of runner v =0

Coefficient of friction ¥=0.7

Let's d be the distance moved by runner till the stop.

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As friction does negetive work causing the runner to stop.

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Answers

Answer:

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\(\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]\)

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\(\[ r_{\text{new}} = \frac{1}{3} \cdot r_{\text{original}} \]\)

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\(\[ F_{\text{new}} = \frac{G \cdot m_1 \cdot m_2}{\left( \frac{1}{3} \cdot r_{\text{original}} \right)^2} \]\)

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Answer:

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Answer:

line graph. A line graph is the best way to show changes in data over time. The geographer can plot the economic growth of one country as a line going up over the 10 years, and the economic decline of the other country as a line going down slightly over the same period. This will allow for a clear visual comparison of the changes in the economies of the two countries over time.

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I don't know what I'm doing wrong I just can't seem to get the answers right. Help please.

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Because the sum of the currents entering and leaving the junction is equal, Kirchhoff's first law is based on the conservation of charge. The algebraic sum of potential drops in a closed circuit must equal zero, according to Kirchhoff's second law. Therefore, it is based on energy conservation.

A stream of charged particles—such as electrons or ions—moving through a conductor for electricity or into empty space is known as an electric current. It is determined by measuring the net rate of electric charge flow through a surface or into a control volume.

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while on a luge run in the olympics the sled (mass=157 kg) rounds a horziontal curve of radius 5.8m with a speed of 18.5 m/s assuming there is no friction what is the normal force exerted by the track on the sled

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In a circular motion the normal force is also called centripetal force. The centripetal force is given by:

\(F=\frac{mv^2}{r}\)

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\(undefined\)

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Answer:

Velocity is a vector whose magnitude is called speed. Collision study needs to analyse the transfer of momentum, which is another vector quantity associated with the velocity vector of each object

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Answers

Answer:

5

Explanation:

The figure shows a jet engine suspended beneath the wing of an airplane. The weight of the engine is 14900 N and acts as shown in the figure. In flight the engine produces a thrust of 61500 N that is parallel to the ground. The rotational axis in the figure is perpendicular to the plane of the paper. With respect to this axis, find the magnitude of the torque due to (a) the weight and (b) the thrust.

The figure shows a jet engine suspended beneath the wing of an airplane. The weight of the engine is

Answers

We have that for the Question, it can be said that With respect to this axis, the magnitude of the torque due to the weight and ,the thrust is

TW=19740N-mTT=130387.39N-m

From the question we are told

The figure shows a jet engine suspended beneath the wing of an airplane. The weight of the engine is 14900 N and acts as shown in the figure. In flight the engine produces a thrust of 61500 N that is parallel to the ground. The rotational axis in the figure is perpendicular to the plane of the paper. With respect to this axis, find the magnitude of the torque due to (a) the weight and (b) the thrust.

a)

Generally the equation for the Torque due to weight  is mathematically given as

\(TW=Engine weight*2.50*sin32\\\\TW=14900*2.50*sin32\)

TW=19740N-m

b)

Generally the equation for the Torque due to thrust  is mathematically given as

\(TT=Engine thrust*2.50*cos32\\\\TT=61500*2.50*cos32\\\\\)

TT=130387.39N-m

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