For Problems # $6$ to #$13,$ you must use scratch paper to show your work.

Note: The phrase "This problem is like $..."$ means the problem uses the same concepts and$/$or formula $($which may need to be algebraically altered$).$ You should NOT assume the problem uses the same identical formula or identical data.

A gas cylinder holds Helium gas. The gas has a Pressure of $1\mathrm{.}82{10}^{7}Pa,$ a Volume of $8\mathrm{.}24m^3,$ and a Temperature of $70F.$ Assume the gas behaves like an Ideal Gas. Calculate the number of moles of Helium within the cylinder. This problem is like Example #$1($pages $2$ & $3)$ in Chapter #$14$ notes.

$7$ to $13)$ A $1\mathrm{.}25-kg$ object is suspended from a ceiling by a spring having a Spring Constant of $12\mathrm{.}5\frac{N}{m}.$ The object is pulled down $0\mathrm{.}250m$ from its Equilibrium Position before being released. This problem is like Examples #$1$ and #$2($pages $2$&$3)$ in Chapter #$15$ notes.

Calculate the object's:

Angular speed $$ in $ra\frac{d}{s}.$

Period $[T]$ in seconds.

Frequency $f$ in $s^{-1}.$

Total Energy $[$ME$]$ in joules.

Maximum speed $v_{\text{m}\text{a}\text{x}}$ in $\frac{m}{s}.$ Write as a positive number.

Maximum Acceleration $a_{\text{m}\text{a}\text{x}}$ in $\frac{m}{s^2}.$ Write as a positive number.

Speed $v$ when the object is $0\mathrm{.}100m$ from its Equilibrium Position $($i$.$e$.,y=0\mathrm{.}100m).$ Write as a positive number.

Spring $2023$