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

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SUMMARY

The discussion focuses on calculating the acceleration of a plank on rolling tubes under the influence of a horizontal force. The plank has a mass of 8 kg, and the tubes have a mass of 2 kg with a radius R. A force of 40 N is applied, and the system rolls without sliding. The key calculations involve determining the speed of the board after it has shifted 2 meters, the acceleration, and the friction forces acting between the board and tubes, as well as between the tubes and the floor.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with rotational dynamics and moment of inertia (Ic = mR^2)
  • Knowledge of kinematics, specifically the relationship between speed, acceleration, and distance
  • Proficiency in calculus, particularly the chain rule for derivatives
NEXT STEPS
  • Calculate the acceleration of the board using the relationship between speed and distance
  • Explore the concept of rolling motion and its implications on friction
  • Investigate the effects of applied forces on rotational systems
  • Learn about the chain rule in calculus for relating different rates of change
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Students studying physics, particularly those focusing on mechanics, as well as educators and anyone interested in understanding the dynamics of rolling motion and force interactions.

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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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