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## Homework Statement

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If particles at B and C of equal mass m are connected by strings to each and to points A and D as shown, all points remaining in the same horizontal plane. If points A and D move with the same acceleration a along parallel paths, solve for the tensile force in each of the strings. Assume that all points retain their initial relative positions.

PLEASE SEE ATTACHMENT

## Homework Equations

__Kinematics- total acceleration:__

**A =**0

**(i)**+ g

**(-j)**+ a

**(j)**+ 0

**(k) =**Ax

**(i)**+ Ay

**(j)**+ Az

**(k)**

__Mechanics:__

**∑F - mA = 0**;

__Magnitude of acceleration due to gravity:__

g =9.81

__Labeling:__

Tension between A & B: Tab, etc

__Coordinate System:__

x to the right

y upwards

z out of the page

## The Attempt at a Solution

__Freebody Diagram on left point mass__

**(EQ1)****∑F1 - mA = 0 =**Tab*cosd(45)

**(-i)**+ Tbc

**(i)**+ Tab*sind(45)

**(j)**- m

**A**

__Freebody Diagram on right point mass__

**(EQ2)****∑F2 - mA = 0 =**Tdc*cosd(45)

**(i)**+ Tbc

**(-i)**+ Tdc*sind(45)

**(j)**- m

**A**

__SOLVING:__

__x-componenets of__

__:__**(EQ1)**and__(EQ2)__Tab = Tdc

__Substituting Tab for Tdc into__

**(EQ2)**y-component:m( g

**(-j)**+ a

**(j)**)

**=**Tab*sind(45)

**(j)**

__Showing y-component of__

**(EQ1)**:m( g

**(-j)**+ a

**(j)**) = Tab*sind(45)

**(j)**

__RESULTING:__

=> Tab = sqrt(2)mAy = Tdc

=> Tbc = mAy

note:

**0**

A =

A =

**(i)**+ g

**(-j)**+ a

**(j)**+ 0

**(k) =**Ax

**(i)**+ Ay

**(j)**+ Az

**(k)**

Ay = -g + a

__My Questions:__

1) The sign of acceleration due to gravity (g) is negative while on the external forces side of the equation, when usually it is negative. Which tells me that there is something wrong with my acceleration term.

2) But, how else can we solve this problem without including the acceleration due to gravity in the total acceleration? Else, I would need to totally neglect it from the solution.

3) If neglected is that the same thing as considering only the dynamic case? i.e. forget the weight = mg. Why? Is there a more intuitive approach?

Thank you.

#### Attachments

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