Kinetics ˗ Body Translating in a Plane

Example: The figure below shows a system consisting of block A of mass m_A, block B

of mass 4m_A, pulley 1 of radius R, and pulley 2 of radius 2R. The system is released

from rest. The coefficient of friction between block A and the horizontal surface is

μ = 1/4. Both pulleys are massless. First determine if block A slides. If it does, then

find the velocities of each block 2 seconds after release. g = 32 ft/sec²

Strategy: Check equilibrium to see if the friction force acting on block A is sufficient to

prevent sliding. Construct FBD’s of both blocks to identify the forces on each block. Use kinematics to relate the accelerations of block A and block B. Apply Euler’s 1^st Law,

F= ma, for each block. Integrate accelerations to find velocities.

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