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## Homework Statement

A pin is constrained to move in a circular slot of radius 39mm. At the same time a slotted bar also constrains the pin to move down with constant velocity 8mm/s. (as shown in attached diagram).

What is the magnitude of the acceleration of the pin for the position shown?

## Homework Equations

NB: instead of using n&t as hinted as suggested, I used x and y coordinate system

## The Attempt at a Solution

time taken for pin to move to position:

[39mm x sin(73)] / 8 mm/s = 4.6619... seconds

position of pin is:

x = 39 - sqrt(39^2 - 8^2*t^2)

so

x = 39 - sqrt(1521 - 64t^2)

y = -8t

pin's velocity is downward hence, it's acceleration is due to sideways movement: (x direction):

x^2 - 2*39*x = -64t^2 **

taking differential of **:

2*x*dx/dt - 2*39*dx/dt = -128t ***

taking differential of ***:

2*dx/dt + 2x*d^2x/dt^2 - 2*39*d^2x/dt^2 = -128 ****

Now, substitute t=4.6613.. into ** to get x = 17.83... mm

then substitute x and t values into *** to get dx/dt = 14.0959... mm/s

then substitute dx/dt into **** to get d^2x/dt^2 = 2.05515...mm/s^2

therefore,

answer: 2.055185 mm/s^2

However, my answer is wrong and I have no idea why?

thank you for any help you can give me

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