If my weight on Earth is 140lbs, what is my mass?
The Correct answer and Explanation is:
To find your mass based on your weight on Earth, you can use the relationship between weight and mass given by the equation:Weight=Mass×g\text{Weight} = \text{Mass} \times gWeight=Mass×g
where:
- Weight is the force due to gravity, measured in pounds (lbs) or newtons (N).
- Mass is the amount of matter in an object, measured in kilograms (kg) or grams (g).
- g is the acceleration due to gravity, which on Earth averages about 9.81 m/s29.81 \, \text{m/s}^29.81m/s2 (or about 32.2 ft/s232.2 \, \text{ft/s}^232.2ft/s2).
Given that your weight on Earth is 140 lbs, we need to convert this weight into mass. However, it’s essential to note that weight in pounds can also be expressed as a force, where 1 lb is approximately equal to 4.448 N. Hence, we can first convert your weight into newtons:Weight in N=140 lbs×4.448 N/lb=622.72 N\text{Weight in N} = 140 \, \text{lbs} \times 4.448 \, \text{N/lb} = 622.72 \, \text{N}Weight in N=140lbs×4.448N/lb=622.72N
Now, using the formula for weight:622.72 N=Mass×9.81 m/s2622.72 \, \text{N} = \text{Mass} \times 9.81 \, \text{m/s}^2622.72N=Mass×9.81m/s2
To find the mass, rearrange the formula:Mass=622.72 N9.81 m/s2≈63.4 kg\text{Mass} = \frac{622.72 \, \text{N}}{9.81 \, \text{m/s}^2} \approx 63.4 \, \text{kg}Mass=9.81m/s2622.72N≈63.4kg
Thus, your mass is approximately 63.4 kg.
Explanation
Understanding the distinction between mass and weight is crucial in physics. Mass is an intrinsic property of matter, indicating the quantity of matter in an object, regardless of its location in the universe. It remains constant regardless of whether you’re on Earth, the Moon, or in space. In contrast, weight is the force exerted by gravity on that mass, and it can vary depending on the gravitational pull of the celestial body you are on.
On Earth, the gravitational acceleration (g) is approximately 9.81 m/s29.81 \, \text{m/s}^29.81m/s2, which provides a reference point for calculating weight. As seen in the calculations above, mass can be determined from weight by dividing by the acceleration due to gravity. Therefore, knowing your weight allows you to easily derive your mass, illustrating the relationship between these two fundamental concepts in physics.