What Minimum Force is Needed to Lift a Wheel Over an Obstacle?

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SUMMARY

The minimum force required to lift a wheel over an obstacle of height h is determined by analyzing the torque around the contact point between the wheel and the obstacle. The torque equation T = rFnet is essential, where r is the radius of the wheel and Fnet is the net force applied horizontally at the axle. The discussion emphasizes the need to consider both the weight of the wheel (W) and the applied force when calculating the torque to ensure it is sufficient to overcome the obstacle. Understanding angular acceleration (α) and its relationship to torque is crucial in this analysis.

PREREQUISITES
  • Understanding of torque and its calculation (T = rFnet)
  • Knowledge of angular acceleration (α) and its implications in rotational dynamics
  • Familiarity with the concepts of weight (W) and force (F) in physics
  • Ability to visualize and draw free-body diagrams for mechanical systems
NEXT STEPS
  • Study the principles of rotational dynamics and torque calculations
  • Learn about the relationship between angular acceleration and torque in rigid body motion
  • Explore the effects of different wheel radii on the force required to lift over obstacles
  • Investigate real-world applications of torque in mechanical engineering
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Students and professionals in physics, mechanical engineering, and anyone interested in understanding the mechanics of lifting objects using torque and force analysis.

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What minimum force F applied horizontally at the axle of the wheel is necessary to raise the wheel over an obstacle of height h? Take r as the radius of the wheel and W as its weight.

We know torque is equal to the radius x perpendicular force
T = rFnet

I think I have to find angular acceleration, α.

T = rma
T = rmα
T = rm(αr)
T = α(mr^2)
ΣT = αΣ(mr^2)

am I on the right track so far?
How do I incorporate height into this, do I want to find angular acceleration in the y direction?
 
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Do they give a picture? If not draw a picture... Draw a wheel standing against a block of height h.

the point where the block and the wheel touch... you want the torque about the point to be zero...

you have two forces involved for this torque... the weight and the horizontal applied force.
 

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