Answer :
Sure! Let's work through the calculations step-by-step:
### Mass Conversion
1. Convert Mass to Kilograms
- You're given that the mass of the object is 0.34 grams.
- To work with the international system of units (SI units), we need to convert grams to kilograms, as the standard unit of mass in the SI unit system is kilograms.
- Conversion is done by dividing the mass in grams by 1000:
[tex]\[
\text{Mass in kilograms} = \frac{0.34 \text{ g}}{1000} = 0.00034 \text{ kg}
\][/tex]
### Velocity Calculation
2. Kinetic Energy Equation
- The kinetic energy ([tex]\(KE\)[/tex]) of an object is given by the formula:
[tex]\[
KE = \frac{1}{2} \cdot \text{mass} \cdot \text{velocity}^2
\][/tex]
- We are given that the kinetic energy is 18 Joules.
3. Rearrange the Formula to Solve for Velocity
- First, rearrange the formula to solve for velocity:
[tex]\[
\text{velocity}^2 = \frac{2 \cdot KE}{\text{mass}}
\][/tex]
- Substitute the known values into the formula (using the mass in kilograms):
[tex]\[
\text{velocity}^2 = \frac{2 \cdot 18 \text{ J}}{0.00034 \text{ kg}}
\][/tex]
4. Calculate Velocity
- [tex]\[
\text{velocity} = \sqrt{\frac{2 \cdot 18}{0.00034}}
\][/tex]
- Calculate the value inside the square root first, then take the square root to find the velocity:
[tex]\[
\text{velocity} = \sqrt{105882.35} \approx 325.40 \text{ m/s}
\][/tex]
So, the velocity of the object is approximately 325.40 meters per second.
### Mass Conversion
1. Convert Mass to Kilograms
- You're given that the mass of the object is 0.34 grams.
- To work with the international system of units (SI units), we need to convert grams to kilograms, as the standard unit of mass in the SI unit system is kilograms.
- Conversion is done by dividing the mass in grams by 1000:
[tex]\[
\text{Mass in kilograms} = \frac{0.34 \text{ g}}{1000} = 0.00034 \text{ kg}
\][/tex]
### Velocity Calculation
2. Kinetic Energy Equation
- The kinetic energy ([tex]\(KE\)[/tex]) of an object is given by the formula:
[tex]\[
KE = \frac{1}{2} \cdot \text{mass} \cdot \text{velocity}^2
\][/tex]
- We are given that the kinetic energy is 18 Joules.
3. Rearrange the Formula to Solve for Velocity
- First, rearrange the formula to solve for velocity:
[tex]\[
\text{velocity}^2 = \frac{2 \cdot KE}{\text{mass}}
\][/tex]
- Substitute the known values into the formula (using the mass in kilograms):
[tex]\[
\text{velocity}^2 = \frac{2 \cdot 18 \text{ J}}{0.00034 \text{ kg}}
\][/tex]
4. Calculate Velocity
- [tex]\[
\text{velocity} = \sqrt{\frac{2 \cdot 18}{0.00034}}
\][/tex]
- Calculate the value inside the square root first, then take the square root to find the velocity:
[tex]\[
\text{velocity} = \sqrt{105882.35} \approx 325.40 \text{ m/s}
\][/tex]
So, the velocity of the object is approximately 325.40 meters per second.
