What Torque is Required for a Hoist Drum to Lift an 8 Tonne Load?

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SUMMARY

The required torque to lift an 8-tonne load with a uniform acceleration of 1.1 m/s² using a hoist drum with a diameter of 2 meters is calculated to be 87.8 kN-m. The mass of the drum is 1 tonne, and its radius of gyration is 750 mm. The torque is derived using the equation T = Iα, where I is the moment of inertia and α is the angular acceleration. Neglecting friction simplifies the calculations, allowing for a straightforward application of Newton's second law.

PREREQUISITES
  • Understanding of Newton's second law (F = MA)
  • Familiarity with rotational dynamics and torque (T = Iα)
  • Knowledge of moment of inertia and radius of gyration
  • Basic skills in free body diagram analysis
NEXT STEPS
  • Study the concept of moment of inertia for various shapes
  • Learn how to derive angular acceleration from linear acceleration
  • Explore free body diagram techniques for complex systems
  • Investigate the effects of friction on torque calculations
USEFUL FOR

Mechanical engineers, physics students, and anyone involved in the design and analysis of hoisting systems will benefit from this discussion.

robbinz
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Homework Statement



Q
A load of mass 8 tonne is to be raised with a uniform acceleration of 1.1 m/s^2 by means of a light cable passing over a hoist drum of 2 m diameter. The drum has a mass of 1 tonne an a radius of gyration of 750 mm. Find the torque required at the drum if friction is neglected.

A
(87.8 KN-M)

Homework Equations



T=Ia = MK^2a ( The a is ment to be alpha )

F=MA

The Attempt at a Solution



Ok so my attempt at the solution was T = Ia(alpha) + F x R ( Taking F=MA )
But it comes out wayyyy wrong.

So obiously I know the solution as I have given it. But I am confused as how to do the working. Can anyone help ?

p.s. First forum post...yayyy :D

Thanks
 
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You need a couple of free body diagrams to start things off. Then write the equations of motion for each mass (the drum, the block being raised) and write the relevant kinematic relations. Then it should all fall into place for you.
 

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