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Andrews [41]
3 years ago
5

The shaft of radius c is subjected to a distributed torque t, measured as torque/unit length of shaft. Shaft A B of length L, fi

xed at B, with x measured from B. Torque t = t sub 0 [1 + (x over L) squared], from t sub 0 at B to 2 t sub 0 at A. The shear modulus is G. Part A Determine the angle of twist at end A. Express your answer as an expression in terms of the variables t0, L, c, and G and any necessary constants.

Physics
1 answer:
tresset_1 [31]3 years ago
7 0

Answer:

Angle of twist;Φ = (to•L²)/Gπc⁴

Explanation:

I have attached the explanation.

However, I used D for radius of shaft against c used in the question. So, if we replace the D with c, we'll have;

Φ = (to•L²)/Gπc⁴

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\texttt{ }

<h3>Further explanation</h3>

Let's recall Elastic Potential Energy and Period of Simple Pendulum formula as follows:

\boxed{E_p = \frac{1}{2}k x^2}

where:

<em>Ep = elastic potential energy ( J )</em>

<em>k = spring constant ( N/m )</em>

<em>x = spring extension ( compression ) ( m )</em>

\texttt{ }

\boxed{T = 2\pi \sqrt{ \frac{L}{g} }}

where:

<em>T = period of simple pendulum ( s )</em>

<em>L = length of pendulum ( m )</em>

<em>g = gravitational acceleration ( m/s² )</em>

Let us now tackle the problem!

\texttt{ }

<u>Given:</u>

initial length of pendulum = L₁ = L

initial mass = M₁ = M

final length of pendulum = L₂ = 2L

final mass = M₂ = 2M

initial period = T₁ = T

<u>Asked:</u>

final period = T₂ = ?

<u>Solution:</u>

T_1 : T_2 = 2\pi \sqrt{ \frac{L_1}{g} }} : 2\pi \sqrt{ \frac{L_2}{g} }}

T_1 : T_2 = \sqrt{L_1} : \sqrt{L_2}

T : T_2 = \sqrt{L} : \sqrt{2L}

T : T_2 = 1 : \sqrt{2}

\boxed {T_2 = \sqrt{2}\ T}

\texttt{ }

<h3>Learn more</h3>
  • Kinetic Energy : brainly.com/question/692781
  • Acceleration : brainly.com/question/2283922
  • The Speed of Car : brainly.com/question/568302
  • Young Modulus : brainly.com/question/9202964
  • Simple Harmonic Motion : brainly.com/question/12069840

\texttt{ }

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Elasticity

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