What Is the Acceleration in an Atwood Machine with Blocks of 396 N and 180 N?

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SUMMARY

The discussion focuses on calculating the acceleration of an Atwood machine consisting of two blocks: Block A weighing 396 N on a table and Block B weighing 180 N hanging off the table. The equations of motion derived from the forces acting on each block include T = ma for Block A and T - Fg = -ma for Block B. The mass of Block B was calculated as 18.349 kg by dividing its weight by the acceleration due to gravity (9.81 m/s²). The final acceleration was incorrectly calculated as 4.905 m/s², indicating a need to treat the masses as a single system to find the net force and correct acceleration.

PREREQUISITES
  • Understanding of Newton's second law of motion (T = ma)
  • Knowledge of gravitational force calculations (Fg = mg)
  • Familiarity with the concept of tension in a pulley system
  • Basic algebra for solving equations
NEXT STEPS
  • Learn how to analyze forces in a pulley system using free-body diagrams
  • Study the concept of net force and its application in systems of connected objects
  • Explore the derivation of acceleration in Atwood machines with varying weights
  • Investigate the effects of friction and pulley mass on acceleration in similar systems
USEFUL FOR

Physics students, educators, and anyone interested in understanding dynamics in mechanical systems, particularly those involving pulleys and connected masses.

wallace13
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In the drawing, there are two blocks connected by a rope and pulley. One block is on the table while the other is hanging off of the table. Block A, with a weight of 396 N, is on the table. Block B is hanging off of the table, and has a weight of 180 N. Ignore all frictional effects and assume the pulley to be massless.
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Find the acceleration of the two blocks.


T= ma
N-Fg= 0
T-Fg=-ma


I made an x and y chart for each of the blocks to show which forces pulled in which direction.

Block A- In the x-direction, there is no Fg or N, but there is T, and the ma is positive. So, I found the equation T= ma... In the y-direction Fg is negative, and there is an N, while ma=0. So I found the equation N-Fg=0.

Block B- There are no forces in the x-direction. In the y-direction, Fg is negative, there is T, and ma is negative, as well. So, I found the equation T- Fg= -ma


I found the mass of block B to be 18.349 kg (I divided 180 by 9.81).

And I substituted all of my known values into my equations...

T-180= -18.349a

I know that T= ma, so I substituted ma for T on the left side of the equation...

18.349a=-18.349a+180

I solved for acceleration and got 4.905, which is the incorrect answer.
 
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First treat the masses as one system... then try to find the Net force acting on the system... then you will be able to find acceleration
 

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