In the equation F = kma, F is measured in N, m in kg, a in ms, and k = 1. When m is measured in mg and a is measured in 5 cm, the value of k should be

In the equation \( F = kma \), we are given that:

- \( F \) is in Newtons (N)
- \( m \) is in kilograms (kg)
- \( a \) is in meters per second squared (m/s\(^2\))
- \( k = 1 \) when \( m \) is in kilograms and \( a \) is in meters per second squared.

Now, when the mass \( m \) is measured in milligrams (mg) and acceleration \( a \) is measured in centimeters per second squared (cm/s\(^2\)), the constant \( k \) must change to account for the different units of measurement. We need to adjust the value of \( k \) to maintain consistency in the equation with Newtons (N) as the unit for force.

### Unit Conversion:
1. **Mass Conversion**: 
   - \( 1 \, \text{kg} = 10^6 \, \text{mg} \)
   - So, \( m \) in milligrams must be divided by \( 10^6 \) to convert it to kilograms: \( m \, (\text{mg}) = \frac{m \, (\text{kg})}{10^6} \).

2. **Acceleration Conversion**: 
   - \( 1 \, \text{m} = 100 \, \text{cm} \)
   - So, \( a \) in centimeters per second squared must be divided by \( 100 \) to convert it to meters per second squared: \( a \, (\text{cm/s}^2) = \frac{a \, (\text{m/s}^2)}{100} \).

### Adjusting \( k \):
To maintain the relationship between force, mass, and acceleration in SI units (where \( k = 1 \)), the constant \( k \) must account for both the conversion from milligrams to kilograms and centimeters to meters.

Thus, we adjust \( k \) as follows:
\[
k = \frac{1}{(10^6) \times (100)} = \frac{1}{10^8}
\]

### Final Answer:
The value of \( k \) should be \( \frac{1}{10^8} \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the value of \( k \) change if acceleration was measured in kilometers per second squared?
2. How can you convert the units of force from Newtons to dynes in this equation?
3. What happens to the constant \( k \) if mass is measured in grams instead of milligrams?
4. How do unit conversions affect the dimensional consistency of physical equations?
5. What is the significance of the constant \( k \) when different unit systems are used?

**Tip**: Always check the units of all variables in an equation to ensure consistency when converting between different unit systems.

Learn how to adjust the constant k in the equation F = kma when mass is measured in milligrams (mg) and acceleration in centimeters per second squared (cm/s²). This guide covers key unit conversions and dimensional analysis, suitable for students in Grades 10-12.

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