What unit of measurement must be used in each variable? F = √3 m = m II II II а:
b. What unit of measurement must be used in each variable? F = √3 m = m II II II а:
The Correct Answer and Explanation is:
a. What unit of measurement must be used in each variable?
Given Equation: F=3 mF = \sqrt{3} \, mF=3m
- F typically stands for force, which is measured in Newtons (N) in the SI system.
- m appears to be a mass, which is measured in kilograms (kg) in the SI system.
However, this equation does not match any standard physical law unless it’s a simplified or abstract form of a relationship. Let’s explore it further to determine the units.
b. Explanation
In physics, consistency in units is crucial to ensure the validity of equations. The equation provided is:F=3 mF = \sqrt{3} \, mF=3m
Here, 3\sqrt{3}3 is a dimensionless constant (approximately 1.732), so it doesn’t affect the units—it simply scales the value.
This means that the units on both sides of the equation must match.
- On the left-hand side, FFF is force, which in the International System of Units (SI) is measured in Newtons (N).
- On the right-hand side, we have 3⋅m\sqrt{3} \cdot m3⋅m, where mmm must have units that, when multiplied by a dimensionless number, result in Newtons.
Let’s recall the definition of a Newton:1 N=1 kg⋅m/s21 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^21N=1kg⋅m/s2
So for the equation F=3 mF = \sqrt{3} \, mF=3m to make sense:
- mmm must also have the units of Newtons, i.e., kg⋅m/s2\text{kg} \cdot \text{m/s}^2kg⋅m/s2, not kilograms.
Therefore, m in this equation is not mass, but rather a force quantity (despite using the variable mmm, which can be confusing). This is an important lesson: variables can represent different physical quantities depending on context.
So, the unit of both F and m in this equation must be Newtons (N).
Final Answer:
- F → Newtons (N)
- m → Newtons (N)
