Why Is the Tension Different in Each Rope of an Accelerating Elevator?

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SUMMARY

The discussion focuses on calculating the tension in ropes supporting two blocks in an upward-accelerating elevator. Given that the elevator accelerates at 1.70 m/s² and each block has a mass of 11.5 kg, the tension in the lower rope (T2) is determined by the weight of the lower block (m2*g), while the upper rope (T1) must account for the combined weight of both blocks plus the additional force due to the elevator's acceleration. The effective gravitational force becomes (g + a), where 'g' is the acceleration due to gravity (9.81 m/s²) and 'a' is the elevator's acceleration.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Basic knowledge of tension in ropes
  • Familiarity with gravitational acceleration (9.81 m/s²)
  • Ability to perform calculations involving forces and mass
NEXT STEPS
  • Calculate the tension in the lower rope using T2 = m2 * (g + a)
  • Calculate the tension in the upper rope using T1 = (m1 + m2) * (g + a)
  • Explore scenarios with different elevator accelerations and their effects on tension
  • Study the implications of varying mass on tension in similar systems
USEFUL FOR

Physics students, engineering students, and anyone interested in understanding dynamics in non-inertial reference frames.

starfish794
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Two blocks are fastened to the ceiling of an elevator. The elevator accelerates upward at 1.70 m/s2. The blocks both have a mass of 11.5 kg. Find the tension in each rope.


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I'm stuck. It seems like the tension on both ropes should be the same but its not.
 
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Think of what the problem would be without the elevator stopped.

There are two blocks of mass m1 (upper mass) and m2 (lower mass). The bottom rope supports the weight of m2, which is m2*g. The top (upper) rope supports weights of both blocks m1* g + m2 * g = (m1+m2)*g.

Now what must one do to adjust the acceleration g if elevator is accelerating upward at 1.7 m/s2?
 

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