Why Did Ignoring the Ground Reaction Force Yield the Correct Torque Calculation?

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SUMMARY

The discussion centers on the calculation of the horizontal force required to initiate rolling of a uniform cylinder with a mass of m kilograms and a radius of 5 meters up a 2-meter step. The correct torque balance was established using the equation 4mg = 3F, leading to the determination of force F without considering the ground reaction force. This outcome demonstrates that, under specific conditions, neglecting the ground reaction force does not affect the accuracy of the torque calculation for this scenario.

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This discussion is beneficial for physics students, mechanical engineers, and anyone interested in understanding the mechanics of rolling objects and torque calculations.

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Homework Statement



A uniform cylinder has mass m kilograms and radius 5 metres. Calculate the magnitude of the horizontal force Fthat needs to be applied on its axis to start it rolling up a step of height 2 metres, as shown in the diagram

Homework Equations



Anticlockwise torque=Clockwise torque at point of contact of cylinder and block

The Attempt at a Solution


4mg=3F gave me the correct value of F needed to start rolling. But I disregarded the reaction force from the ground and still got the correct answer. How is that possible that disregarding the moment by the reaction on the cylinder from the flat ground had no effect on the answer. Picture of the question has been uploaded too.
 

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Asad Raza said:
How is that possible that disregarding the moment by the reaction on the cylinder from the flat ground had no effect on the answer.
Imagine increasing F slowly until the cylinder just starts to lift. What would be the normal force from the ground then?
 
haruspex said:
Imagine increasing F slowly until the cylinder just starts to lift. What would be the normal force from the ground then?
Ooops! Got it :')
 

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