Long Handled

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May 2nd, 2009 admin Leave a comment Go to comments

short or long handles for lawn mower why prove it mathematically?

its a physics question asking will i need short or long handle for lawn mower and why?

There's something in that question that describes what "short" and "long" mean, and how the mower is intended to be used. Some of the information is probably supposed to be common sense. Anybody who has actually mowed a lawn knows that a handle too short or too long isn't practical.

The physics of the situation is that you want to push the mower without lifting the front or back wheels of the mower. That means no "upward" torque about the front axles and no "downward" torque about the rear axles. To do this, your applied force to the handle needs to be somewhere between the wheels. The smallest angle from the horizontal gives the greatest forward force, so aiming close to the front wheels is best. A good mower will have the handle adjusted at that angle, so there's no torque where the handle attaches to the mower, either.

Mathmatically, if the force is directed at an angle θ below horizontal, then:

Fx = F*cos θ is maximum when θ = 0

...is the forward force. That may be part of the question. If both handles come up to the same comfortable height above ground, which one makes the smaller angle θ? A short handle or a long one?