Convert 1 neuron into dyne using dimensional analysis.
Understand the Problem
The question is asking for the conversion of a unit of force, 'neuron', into another unit, 'dyne', using dimensional analysis. This involves understanding the relationship between these two units and how they can be converted based on their definitions.
Answer
1 neutron is equal to $10^{-4}$ dynes.
Answer for screen readers
1 neutron (n) is equal to $10^{-4}$ dynes (d).
Steps to Solve
- Identify the definitions of the units The first step is to identify the definitions of the units involved.
1 neutron (n) is defined as: $$ 1 n = 10^{-9} \text{ N} $$
1 dyne (d) is defined as: $$ 1 d = 10^{-5} \text{ N} $$
- Set up the conversion factor To convert from neutrons to dynes, we can set up the conversion factor using the definitions of the units.
We want to convert 1 neutron to dynes, which can be expressed as: $$ 1 n = \frac{10^{-9} \text{ N}}{10^{-5} \text{ N}} \times 1 d $$
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Calculate the conversion Now, we can calculate the conversion: $$ 1 n = \frac{10^{-9}}{10^{-5}} d $$
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Simplify the expression To simplify, subtract the exponents: $$ 1 n = 10^{-9 + 5} d = 10^{-4} d $$
This means: $$ 1 n = 0.0001 d $$
1 neutron (n) is equal to $10^{-4}$ dynes (d).
More Information
The neutron is a very small unit of force, while the dyne is also a smaller unit of force but used often in physics, particularly in the cgs (centimeter-gram-second) system. Understanding these conversions is crucial when dealing with physics problems that involve force.
Tips
- Confusing the numerical values of the force definitions. Always double-check the definitions to ensure the correct values are used.
- Not properly handling the exponent subtraction. Make sure to subtract the powers accurately when simplifying the expressions.
