To determine the acceleration produced on a mass of 200 grams when a force of 10 Newtons is exerted on it, we will use Newton's second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration ([tex]\( F = m \cdot a \)[/tex]).
Let's proceed step-by-step:
1. Convert the mass from grams to kilograms:
- The mass given is 200 grams.
- Since there are 1000 grams in a kilogram, we convert the mass as follows:
[tex]\[
\text{mass in kilograms} = \frac{200 \text{ grams}}{1000} = 0.2 \text{ kilograms}
\][/tex]
2. Write down the given force using Newton's second law:
- The force ([tex]\( F \)[/tex]) is given as 10 Newtons.
3. Rearrange Newton's second law to solve for acceleration ([tex]\( a \)[/tex]):
- The formula is [tex]\( F = m \cdot a \)[/tex].
- To solve for [tex]\( a \)[/tex] (acceleration), we rearrange the formula to:
[tex]\[
a = \frac{F}{m}
\][/tex]
4. Substitute the known values into the equation:
- The force [tex]\( F \)[/tex] is 10 Newtons.
- The mass [tex]\( m \)[/tex] is 0.2 kilograms.
[tex]\[
a = \frac{10 \text{ Newtons}}{0.2 \text{ kilograms}}
\][/tex]
5. Calculate the acceleration:
- Perform the division:
[tex]\[
a = 50.0 \text{ meters per second squared}
\][/tex]
Therefore, an acceleration of [tex]\( 50.0 \ \text{m/s}^2 \)[/tex] is produced when a force of 10 Newtons is exerted on a mass of 200 grams.
