Determine the acceleration of the 80 kg block

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The discussion focuses on determining the acceleration of an 80 kg block as a 65 kg man climbs a rope with an acceleration of 0.25 m/s² relative to the rope. Two equations are derived from free body diagrams: one for the tension in the rope acting on the block and another for the man. It is assumed that the acceleration of the block and the rope are the same. The relationship between the man's acceleration and the block's acceleration is established, leading to the conclusion that the block's acceleration can be calculated using the difference in their accelerations. The key takeaway is that the acceleration of the block can be found by adjusting for the man's climbing acceleration.
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The 65 kg man climbs up the rope with an acceleration of 0.25 m/s^2, measured relative to the rope. Determine the acceleration of the 80 kg block.

This is just a man climbing up a rope on the right with the rope wrapped over a pulley and on the other side a block hangs.

ok so the two equations I came up with from the FBD's are

T-784.8 = 80 * (accel. of block)

T - 637.65 = 65 * (accel. of man)

An assumption I made is the accel. of block and accel of rope must be the same.

Ok so the acceleration of the man with respect to the rope = 0.25? How can I use this piece of information to determine the acceleration of the block.
 
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Hi ur5pointos2sl! :smile:

(try using the X2 tag just above the Reply box :wink:)

a - b = 0.25 m/s2, where b is the acceleration of the block (upward). :smile:
 
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