To determine the centripetal force exerted on the object situated on the outside of the platter, we need to follow a series of steps carefully incorporating unit conversions where necessary:
1. Given Values:
- Mass ([tex]\(m\)[/tex]) of the object: [tex]\(1.29 \text{ kg}\)[/tex]
- Speed ([tex]\(v\)[/tex]): [tex]\(0.0213 \text{ m/s}\)[/tex]
- Radius ([tex]\(r\)[/tex]): [tex]\(14.2 \text{ cm}\)[/tex]
2. Convert Radius to Meters:
The radius is given in centimeters, so we need to convert it to meters. There are 100 centimeters in a meter, thus:
[tex]\[
r = \frac{14.2 \text{ cm}}{100} = 0.142 \text{ m}
\][/tex]
3. Centripetal Force Formula:
The formula for centripetal force ([tex]\(F_c\)[/tex]) is:
[tex]\[
F_c = \frac{mv^2}{r}
\][/tex]
where:
- [tex]\(m\)[/tex] is the mass
- [tex]\(v\)[/tex] is the speed
- [tex]\(r\)[/tex] is the radius
4. Substitute the Given Values:
[tex]\[
F_c = \frac{1.29 \times (0.0213)^2}{0.142}
\][/tex]
5. Calculate the Numerator ([tex]\(mv^2\)[/tex]):
[tex]\[
mv^2 = 1.29 \times (0.0213)^2 \approx 1.29 \times 0.00045369 = 0.00058526 \text{ kg m}^2\text{/s}^2
\][/tex]
6. Calculate the Centripetal Force:
[tex]\[
F_c = \frac{0.00058526}{0.142} \approx 0.004120 \text{ N}
\][/tex]
7. Express the Result in Scientific Notation:
To express [tex]\(0.004120 \text{ N}\)[/tex] in scientific notation, we rewrite it as follows:
[tex]\[
0.004120 \text{ N} = 4.12 \times 10^{-3} \text{ N}
\][/tex]
Thus, the centripetal force exerted on the object situated on the outside of the platter is:
[tex]\[
4.12 \times 10^{-3} \text{ N}
\][/tex]
So, the answer is:
[tex]\[
4.12 \times 10^{-3} \text{ N}
\][/tex]
