Move along, Larry

Classical Mechanics Level 2

Two men, Joe and Larry, are carrying a 24 24 foot long board with it's weight evenly distributed along it's length.

Joe is at one end, and Larry is x x feet from the center, between the center and the opposite end.

If we graph the percentage of the weight Larry carries as a function of x x , what behavior does the graph exhibit?

Linear sloping down Contains a point of inflection Concave up Linear sloping up Concave down Constant

Geoff Pilling by Geoff Pilling , 53, USA

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1 solution

Geoff Pilling
Jan 2, 2019

Solution (inspired by @Brian Charlesworth )...

Balancing the torque around Joe's end, the weight of the board will be at its center, so...

If F F is the force Larry must exert and W W is the weight of the board, then

12 W = F ( 12 + x ) 12W = F(12 + x)

F = 12 W 12 + x F = \dfrac{12W}{12+x}

This function is concave up.

2 Helpful 0 Interesting 1 Brilliant 0 Confused

Thanks for the reference! I'm guessing that you just meant " x x feet from the center" rather than "other center". I suspect you were debating between measuring from either the "other end" or the "center", but either way the curve would be concave up.

Brian Charlesworth - 2 years, 5 months ago

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Good catch... I've updated the problem.

Geoff Pilling - 2 years, 5 months ago

Concave up is smiling mouth or smiling eyes?

Saya Suka - 2 years ago

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