How Do You Calculate the Acceleration of a Board on Rolling Tubes?

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To calculate the acceleration of a board on rolling tubes, one must first determine the speed of the board after it has shifted a distance of 2 meters. The relationship between speed and distance can be utilized to find acceleration using the chain rule, specifically by deriving speed as a function of distance. Additionally, the frictional forces between the board and the tubes, as well as between the tubes and the floor, need to be considered in the overall dynamics of the system. The applied horizontal force of 40 N plays a crucial role in these calculations. Understanding these principles will help in accurately determining the acceleration of the board.
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Homework Statement



Plank of mass M = 8 kgr is installed on the same two tubes (very small
thickness) radius R and mass m = 2 kgr. Initially the system property. A horizontal
force F = 40 N applied to the board and the tubes rolled without sliding (Ic = mR^2).
When the board shifted s = 2m on the ground calculate:

a. the speed of the board
b. the acceleration of the board
c. the friction between board and the tubes
d. the friction between tubes and floor

The Attempt at a Solution



Ι have found the speed of the board but i don't know how to find the acceleration.
 

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Welcome to PF!

Hi costas! Welcome to PF! :smile:
costas said:
Ι have found the speed of the board but i don't know how to find the acceleration.

If you have found v as a function of s, then obviously you know how to get dv/ds, and you can then get dv/dt by using the chain rule :wink:
 

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