6. Question

Based on experimental observations, the acceleration of a particle is defined by the relationa = -( 0.1 + sin(x/b) ),where a and

yKpoI14uk [10]

Answer:

a) v = +/- 0.323 m/s

b) x = -0.080134 m

c) v = +/- 1.004 m/s

Explanation:

Given:

a = - (0.1 + sin(x/b))

b = 0.8

v = 1 m/s @ x = 0

Find:

(a) the velocity of the particle when x = -1 m

(b) the position where the velocity is maximum

(c) the maximum velocity.

Solution:

- We will compute the velocity by integrating a by dt.

a = v*dv / dx = - (0.1 + sin(x/0.8))

- Separate variables:

v*dv = - (0.1 + sin(x/0.8)) . dx

-Integrate from v = 1 m/s @ x = 0:

0.5(v^2) = - (0.1x - 0.8cos(x/0.8)) - 0.8 + 0.5

0.5v^2 = 0.8cos(x/0.8) - 0.1x - 0.3

- Evaluate @ x = -1

0.5v^2 = 0.8 cos(-1/0.8) + 0.1 -0.3

v = sqrt (0.104516)

v = +/- 0.323 m/s

- v = v_max when a = 0:

-0.1 = sin(x/0.8)

x = -0.8*0.1002

x = -0.080134 m

- Hence,

v^2 = 1.6 cos(-0.080134/0.8) -0.6 -0.2*-0.080134

v = sqrt (0.504)

v = +/- 1.004 m/s

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Which of the following describes the most direct and attainable way to reduce pollution in the environment?

kirill115 [55]

Answer:

i think its A. increasing research to find alternative natural resources for the future

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Read 2 more answers

Deidre has just moved from the sales department into the finance department. On her first day in her new role, she receives an e

melisa1 [442]

Answer:

d. The company uses role-based access control and her user account hasn't been migrated into the correct group(s) yet

Explanation:

Since Deidre is accessing her e-mail there appears to be nothing wrong with her account or password. Since her role is new, most likely the problem is associated with her new role.

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Write the heat equation for each of the following cases:

jok3333 [9.3K]

Answer:

Explanation:

a) the steady-state, 1-D incompressible and no energy generation equation can be expressed as follows:

$\dfrac{\partial^2T}{\partial x^2}= \ 0 \ ; \ if \ T = f(x) \\ \\ \dfrac{\partial^2T}{\partial y^2}= \ 0 \ ; \ if \ T = f(y) \\ \\ \dfrac{\partial^2T}{\partial z^2}= \ 0 \ ; \ if \ T = f(z)$

b) For a transient, 1-D, constant with energy generation

suppose T = f(x)

Then; the equation can be expressed as:

$\dfrac{\partial^2T}{\partial x^2} + \dfrac{Q_g}{k} = \dfrac{1}{\alpha} \dfrac{dT}{dC}$

where;

$Q_g$ = heat generated per unit volume

$\alpha$ = Thermal diffusivity

c) The heat equation for a cylinder steady-state with 2-D constant and no compressible energy generation is:

$\dfrac{1}{r}\times \dfrac{\partial}{\partial r }( r* \dfrac{\partial \ T }{\partial \ r}) + \dfrac{\partial^2 T}{\partial z^2 }= 0$

where;

The radial directional term = $\dfrac{1}{r}\times \dfrac{\partial}{\partial r }( r* \dfrac{\partial \ T }{\partial \ r})$ and the axial directional term is $\dfrac{\partial^2 T}{\partial z^2 }$

d) The heat equation for a wire going through a furnace is:

$\dfrac{\partial ^2 T}{\partial z^2} = \dfrac{1}{\alpha}\Big [\dfrac{\partial ^2 T}{\partial ^2 t}+ V_z \dfrac{\partial ^2T}{\partial ^2z} \Big ]$

since;

the steady-state is zero, Then:

$\dfrac{\partial ^2 T}{\partial z^2} = \dfrac{1}{\alpha}\Big [ V_z \dfrac{\partial ^2T}{\partial ^2z} \Big ]$ '

e) The heat equation for a sphere that is transient, 1-D, and incompressible with energy generation is:

$\dfrac{1}{r} \times \dfrac{\partial}{\partial r} \Big ( r^2 \times \dfrac{\partial T}{\partial r} \Big ) + \dfrac{Q_q}{K} = \dfrac{1}{\alpha}\times \dfrac{\partial T}{\partial t}$

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HELP PLS Leaders usually start as

Kazeer [188]

Team members and the work from ther

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