To calculate the kinetic energy (KE) of the micrometeor, you can use the formula:
\[ KE = \frac{1}{2} mv^2 \]
Where:
- \( m \) is the mass in kilograms
- \( v \) is the velocity in meters per second
First, convert the mass from grams to kilograms:
\[ 0.005 \text{ grams} = 0.005 , \text{g} \times \frac{1 , \text{kg}}{1000 , \text{g}} = 0.000005 , \text{kg} \]
Next, substitute the values into the formula, using \( v = 21,000 , \text{m/s} \):
\[ KE = \frac{1}{2} \times 0.000005 , \text{kg} \times (21000 , \text{m/s})^2 \]
First, calculate \( (21000 , \text{m/s})^2 \):
\[ (21000)^2 = 441000000 \]
Now substitute this value into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 0.000005 , \text{kg} \times 441000000 \]
Now compute:
\[ KE = 0.0000025 \times 441000000 = 1102.5 , \text{J} \]
Therefore, the kinetic energy when the micrometeor enters Earth’s atmosphere is:
1,102.5 J.
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