Answer:
the rotational inertia of the cylinder = 4.85 kgm²
the mass moved 7.942 m/s
Explanation:
Formula for calculating Inertia can be expressed as:
![I =\frac{1}{2}mR^2](https://tex.z-dn.net/?f=I%20%3D%5Cfrac%7B1%7D%7B2%7DmR%5E2)
For calculating the rotational inertia of the cylinder ; we have;
![I = \frac{1}{2}m_pR^2](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B1%7D%7B2%7Dm_pR%5E2)
![I = \frac{1}{2}*10.53*(0.96)^2](https://tex.z-dn.net/?f=I%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A10.53%2A%280.96%29%5E2)
![I=5.265*(0.96)^2](https://tex.z-dn.net/?f=I%3D5.265%2A%280.96%29%5E2)
![I=4.852224](https://tex.z-dn.net/?f=I%3D4.852224)
I ≅ 4.85 kgm²
mg - T ma and RT = I ∝
T = ![\frac{Ia}{R^2}](https://tex.z-dn.net/?f=%5Cfrac%7BIa%7D%7BR%5E2%7D)
![a = \frac{g}{1+\frac{I}{mR^2}}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7Bg%7D%7B1%2B%5Cfrac%7BI%7D%7BmR%5E2%7D%7D)
![a = \frac{9.8}{1+\frac{4.85}{3.9*(0.96)^2}}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B9.8%7D%7B1%2B%5Cfrac%7B4.85%7D%7B3.9%2A%280.96%29%5E2%7D%7D)
a = 4.1713 m/s²
Using the equation of motion
![v^2 = u^2+2as \\ \\ v^2 = 2as \\ \\ v = \sqrt{2*a*s} \\ \\ v= \sqrt{2*4.1713*7.56} \\ \\ v = 7.942 \ m/s](https://tex.z-dn.net/?f=v%5E2%20%3D%20u%5E2%2B2as%20%5C%5C%20%5C%5C%20v%5E2%20%3D%202as%20%5C%5C%20%5C%5C%20v%20%3D%20%5Csqrt%7B2%2Aa%2As%7D%20%5C%5C%20%5C%5C%20v%3D%20%5Csqrt%7B2%2A4.1713%2A7.56%7D%20%5C%5C%20%5C%5C%20v%20%3D%207.942%20%5C%20m%2Fs)
Particles vibrate parallel to the direction the sound travels. It's a longitudinal wave.
Answer:
The force of the nail pushing in the opposite direction