Torque and force

2010-11-13 9:07 am
A wheel of mass M has radius R. It is standing vertically on the floor , and we wantto exert a horizontal force F at its axle so that it will climb a step against which it rests. The step has height h where h<R What minimum force F is needed?
更新1:

The Clockwise motion = anti , menas there is no torque , means there is no rotation? So how can it against the step.

回答 (3)

2010-11-14 8:03 am
✔ 最佳答案
Taking moment about the point of contact of the wheel at the step.
Perpendicular distance of F from the point of contant = (R - h)
Perpendicular distance of the weight of the wheel from the point of contact
= square-root[R^2 - (R-h)^2]
= square-root[h(2R-h)]

Hence, F x (R-h) = Mg.(square-root[h(2R-h)])
where g is the acceleration due to gravity
i.e. F = Mg.(square-root[h(2R-h)]/(R-h))
2010-11-14 5:31 am
2 forces actually
2010-11-14 4:30 am
This question is quite difficult, three forces acting at different positions which can not be drawn on one line.

2010-11-14 20:51:38 補充:
I guess there should have net torque for the wheel to rotate and ''climb'' the step.

3 forces : weight, applied force, normal reaction from the contact between the step and the wheel, but if the question does not tell if there is also the forth force which is friction.


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