Atwood machine, block on cart: compute the minimum static friction coefficient to avoid slipping.

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  • Опубліковано 31 лип 2024
  • Atwood machine, block on cart: compute the minimum static friction coefficient to avoid slipping.
    We are given a horizontal Atwood machine with a hanging mass causing the system to accelerate. On the horizontal track, a cart rolls with negligible friction, but there is a block on top of the cart. The block accelerates without slipping due to the presence of a static friction force.
    We start by solving for tension and acceleration in the Atwood machine, and this is done in the standard way: diagram forces and apply Newton's second law to each moving piece of the Atwood machine, taking care to use the same direction of acceleration in each analysis as the positive direction. The block-on-cart is treated as one total mass here, since it's all accelerating at the same rate.
    Once we have the acceleration, we can figure out the net force on the block, and this allows us to compute the static friction force -- that's the horizontal force that accelerates the block!
    Finally, we assume the static friction force is at its maximum value, and this corresponds to the minimum coefficient of static friction to keep the block locked in place (any smaller coefficient, and the maximum possible static friction force would be exceeded as the system accelerates). We use the normal force and the friction force to solve for the minimum coefficient of static friction, and we're done!

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