A man weighs 84.8 N. What is his mass in kilograms?
Understand the Problem
The question is asking to convert the weight of a man given in newtons (84.8 N) into mass in kilograms. To solve this, we will use the relationship between weight (force) and mass defined by the equation W = m * g, where W is weight, m is mass, and g is the acceleration due to gravity (approximately 9.81 m/s²).
Answer
The man's mass is approximately $8.64 \, \text{kg}$.
Answer for screen readers
The man's mass is approximately $8.64 , \text{kg}$.
Steps to Solve
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Identify the Formula To convert weight (W) in newtons to mass (m) in kilograms, we use the equation: $$ W = m \cdot g $$ where ( g ) is the acceleration due to gravity (approximately ( 9.81 , \text{m/s}^2 )).
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Rearrange the Formula To find mass, rearrange the equation to solve for ( m ): $$ m = \frac{W}{g} $$
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Substitute the Given Values Insert the given weight into the rearranged formula: $$ m = \frac{84.8 , \text{N}}{9.81 , \text{m/s}^2} $$
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Calculate the Mass Now, perform the calculation: $$ m = \frac{84.8}{9.81} \approx 8.64 , \text{kg} $$
The man's mass is approximately $8.64 , \text{kg}$.
More Information
This calculation uses the relationship between weight and mass. By dividing the weight by the acceleration due to gravity, we can obtain the mass in kilograms.
Tips
- Ignoring Units: Always check that weight is in newtons and gravity is in ( \text{m/s}^2 ) to avoid unit conversion errors.
- Wrong Gravity Value: Ensure that the value of ( g ) (9.81 m/s²) is used consistently unless specified differently.
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