Answer:
1a. 0.030 s
1b. 15×10¹⁰ kg m²/s²
Explanation:
Remember order of operations (PEMDAS).
1a. [tex]T_{s} =2\pi \sqrt{\frac{4.5\times10^{-2}\ kg }{2.0\times10^{3}\ kg/s^{2} } }[/tex]
Start by dividing the numbers, the powers of 10 (using exponent rules), and the units.
[tex]T_{s} =2\pi \sqrt{\frac{4.5}{2.0} \frac{10^{-2}}{10^{3}} \frac{kg}{kg/s^{2}}}\\T_{s} =2\pi \sqrt{2.25 \times10^{-2-3}\ s^{2}}\\T_{s} =2\pi \sqrt{2.25 \times10^{-5}\ s^{2}}[/tex]
Take the square root:
[tex]T_{s} =2\pi \sqrt{2.25} \sqrt{10^{-5}} \sqrt{s^{2}}\\T_{s} =2\pi \times1.5 \times10^{-2.5}\ s[/tex]
Finally, multiply (you'll need a calculator):
[tex]T_{s} \approx 0.030\ s[/tex]
1b. [tex]K=\frac{1}{2} (6.6\times10^{2}\ kg)(2.11\times10^{4}\ m/s)^{2}[/tex]
Start by squaring the last term:
[tex]K=\frac{1}{2} (6.6\times10^{2}\ kg)(2.11^{2}\times10^{4\times2}\ m^{2}/s^{2})\\K=\frac{1}{2} (6.6\times10^{2}\ kg)(4.4521\times10^{8}\ m^{2}/s^{2})[/tex]
Now like before, multiply the numbers, the powers of 10 (using exponent rules), and the units:
[tex]K=\frac{1}{2} (6.6\times4.4521)(10^{2+8})(kg\ m^{2}/s^{2})\\K=\frac{1}{2} (29.38386)(10^{10})(kg\ m^{2}/s^{2})\\K\approx15\times10^{10}\ kg\ m^{2}/s^{2}[/tex]
