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Question 1.3: The Weight of One Pound-Mass Using unity conversion ratios, ...

The Weight of One Pound-Mass

Using unity conversion ratios, show that 1.00 lbm weighs 1.00 lbf on earth (Fig. 1-17).

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A mass of 1.00 \mathrm{lbm} is subjected to standard earth gravity. Its weight in Ibf is to be determined.
Assumptions Standard sea-level conditions are assumed.
Properties The gravitational constant is g=32.174 \mathrm{ft} / \mathrm{s}^{2}.
Analysis We apply Newton’s second law to calculate the weight (force) that corresponds to the known mass and acceleration. The weight of any object is equal to its mass times the local value of gravitational acceleration. Thus,

W=m g=(1.00 \mathrm{lbm})\left(32.174 \mathrm{ft} / \mathrm{s}^{2}\right)\left(\frac{1 \mathrm{lbf}}{32.174 \mathrm{lbm} \cdot \mathrm{ft} / \mathrm{s}^{2}}\right)=1.00 \mathrm{lbf}

 

Discussion The quantity in large parentheses in this equation is a unity conversion ratio. Mass is the same regardless of its location. However, on some other planet with a different value of gravitational acceleration, the weight of 1 \mathrm{lbm} would differ from that calculated here.

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