Efficiency= (Work Input/Work Output) x 100
Answer:
a
![m = 0.169 \ kg](https://tex.z-dn.net/?f=m%20%20%3D%200.169%20%5C%20kg)
b
![|v_{max} |= 0.5653 \ m/s](https://tex.z-dn.net/?f=%7Cv_%7Bmax%7D%20%7C%3D%20%200.5653%20%5C%20m%2Fs)
Explanation:
From the question we are told that
The spring constant is ![k = 14 \ N/m](https://tex.z-dn.net/?f=k%20%3D%20%2014%20%5C%20N%2Fm)
The maximum extension of the spring is ![A = 6.0 \ cm = 0.06 \ m](https://tex.z-dn.net/?f=A%20%3D%20%206.0%20%5C%20cm%20%20%3D%20%200.06%20%5C%20m)
The number of oscillation is ![n = 30](https://tex.z-dn.net/?f=n%20%20%3D%20%2030)
The time taken is ![t = 20 \ s](https://tex.z-dn.net/?f=t%20%20%3D%20%2020%20%5C%20s)
Generally the the angular speed of this oscillations is mathematically represented as
![w = \frac{2 \pi}{T}](https://tex.z-dn.net/?f=w%20%3D%20%5Cfrac%7B2%20%5Cpi%7D%7BT%7D)
where T is the period which is mathematically represented as
![T = \frac{t}{n}](https://tex.z-dn.net/?f=T%20%20%3D%20%20%5Cfrac%7Bt%7D%7Bn%7D)
substituting values
![T = \frac{20}{30 }](https://tex.z-dn.net/?f=T%20%20%3D%20%20%5Cfrac%7B20%7D%7B30%20%7D)
![T = 0.667 \ s](https://tex.z-dn.net/?f=T%20%20%3D%200.667%20%5C%20s)
Thus
![w = \frac{2 * 3.142 }{ 0.667}](https://tex.z-dn.net/?f=w%20%3D%20%5Cfrac%7B2%20%2A%203.142%20%7D%7B%200.667%7D)
![w = 9.421 \ rad/s](https://tex.z-dn.net/?f=w%20%3D%20%209.421%20%5C%20rad%2Fs)
this angular speed can also be represented mathematically as
![w = \sqrt{\frac{k}{m} }](https://tex.z-dn.net/?f=w%20%3D%20%20%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%20%7D)
=> ![m =\frac{k }{w^2}](https://tex.z-dn.net/?f=m%20%20%3D%5Cfrac%7Bk%20%7D%7Bw%5E2%7D)
substituting values
![m =\frac{ 15 }{(9.421)^2}](https://tex.z-dn.net/?f=m%20%20%3D%5Cfrac%7B%2015%20%7D%7B%289.421%29%5E2%7D)
![m = 0.169 \ kg](https://tex.z-dn.net/?f=m%20%20%3D%200.169%20%5C%20kg)
In SHM (simple harmonic motion )the equation for velocity is mathematically represented as
![v = - Awsin (wt)](https://tex.z-dn.net/?f=v%20%3D%20%20-%20Awsin%20%28wt%29)
The velocity is maximum when
![v_{max} = - A* w](https://tex.z-dn.net/?f=v_%7Bmax%7D%20%3D%20-%20%20A%2A%20w)
=> ![|v_{max} |= A* w](https://tex.z-dn.net/?f=%7Cv_%7Bmax%7D%20%7C%3D%20%20A%2A%20w)
=> ![|v_{max} |= 0.06 * 9.421](https://tex.z-dn.net/?f=%7Cv_%7Bmax%7D%20%7C%3D%20%20%200.06%20%2A%209.421)
=> ![|v_{max} |= 0.5653 \ m/s](https://tex.z-dn.net/?f=%7Cv_%7Bmax%7D%20%7C%3D%20%200.5653%20%5C%20m%2Fs)
Answer: The multiplication factor is 72.136 cm. This will give you the unit conversion when multiplied with 28.4 inch
Explanation:
1 inch = 2.54 cm
28.4 inches = x cm
Xcm= (28.4 inches × 2.54cm)/1 inch
X= 72.136