Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Relationship Between Weight and Mass
Weight is the force exerted on an object due to gravity, while mass is the amount of matter in an object. On Earth, we can convert weight to mass using the gravitational acceleration.
Step 3:: Recall the Gravitational Acceleration on Earth
The standard gravitational acceleration on Earth is $$g = 9.8 \frac{mathrm{m/s}^{2}}
Step 4:: Convert Pounds to Newtons
140 \text{ lbs} \times \frac{4.448 \text{ N}}{1 \text{ lb}} = 623.52 \text{ N}
First, convert 140 lbs to Newtons:
Step 5:: Use the Weight-Mass Relationship Formula
W = m \times g
The formula relating weight (W), mass (m), and gravitational acceleration (g) is:
Step 6:: Solve for Mass
m = \frac{W}{g} = \frac{623.52 \text{ N}}{9.8 \frac{mathrm{m/s}^{2}}} = 63.63 \text{ kg}
Rearrange the formula to solve for mass:
Final Answer
Your mass is 63.63 \text{ kg}.
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