# Curvilinear n&t motion question engineering mechanics

## 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,

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

Last edited:

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Hi kasthuri, I don't know if I could help you but you apparently forgot to actually attach the "attached diagram" :)
side question: are you familiar with the lagrangian formalism ?

Sorry and thanks for telling me! I've attached it on my reply
Also, I don't know about the lagrangian formalism.
:)

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Hi, Katsthuri, sorry for my silly question about the lagrangian, I thought you were resolving a different kind of problem and I didn't read your whole post to well since the picture wasn't available