Question

Can someone help me solve these two equations?

Answer 1

1a. 0.030 s

1b. 15×10¹⁰ kg m²/s²

Step-by-step explanation:

Remember order of operations (PEMDAS).

1a.
`T_(s) =2\pi \sqrt{(4.5*10^(-2)\ kg )/(2.0*10^(3)\ kg/s^(2) ) }`

Start by dividing the numbers, the powers of 10 (using exponent rules), and the units.

`T_(s) =2\pi \sqrt{(4.5)/(2.0) (10^(-2))/(10^(3)) (kg)/(kg/s^(2))}\\T_(s) =2\pi \sqrt{2.25 *10^(-2-3)\ s^(2)}\\T_(s) =2\pi \sqrt{2.25 *10^(-5)\ s^(2)}`

Take the square root:

`T_(s) =2\pi √(2.25) \sqrt{10^(-5)} \sqrt{s^(2)}\\T_(s) =2\pi *1.5 *10^(-2.5)\ s`

Finally, multiply (you'll need a calculator):

`T_(s) \approx 0.030\ s`

1b.
`K=(1)/(2) (6.6*10^(2)\ kg)(2.11*10^(4)\ m/s)^(2)`

Start by squaring the last term:

`K=(1)/(2) (6.6*10^(2)\ kg)(2.11^(2)*10^(4*2)\ m^(2)/s^(2))\\K=(1)/(2) (6.6*10^(2)\ kg)(4.4521*10^(8)\ m^(2)/s^(2))`

Now like before, multiply the numbers, the powers of 10 (using exponent rules), and the units:

`K=(1)/(2) (6.6*4.4521)(10^(2+8))(kg\ m^(2)/s^(2))\\K=(1)/(2) (29.38386)(10^(10))(kg\ m^(2)/s^(2))\\K\approx15*10^(10)\ kg\ m^(2)/s^(2)`