(a) 6.04 rev/s
The speed of the ball is given by:
![v=\omega r](https://tex.z-dn.net/?f=v%3D%5Comega%20r)
where
is the angular speed
r is the distance of the ball from the centre of the circle
In situation 1), we have
![\omega=8.13 rev/s \cdot 2\pi = 51.0 rad/s](https://tex.z-dn.net/?f=%5Comega%3D8.13%20rev%2Fs%20%5Ccdot%202%5Cpi%20%3D%2051.0%20rad%2Fs)
r = 0.600 m
So the speed of the ball is
![v=(51.0 rad/s)(0.600 m)=30.6 m/s](https://tex.z-dn.net/?f=v%3D%2851.0%20rad%2Fs%29%280.600%20m%29%3D30.6%20m%2Fs)
In situation 2), we have
![\omega=6.04 rev/s \cdot 2\pi = 37.9 rad/s](https://tex.z-dn.net/?f=%5Comega%3D6.04%20rev%2Fs%20%5Ccdot%202%5Cpi%20%3D%2037.9%20rad%2Fs)
r = 0.900 m
So the speed of the ball is
![v=(37.9 rad/s)(0.900 m)=34.1 m/s](https://tex.z-dn.net/?f=v%3D%2837.9%20rad%2Fs%29%280.900%20m%29%3D34.1%20m%2Fs)
So, the ball has greater speed when rotating at 6.04 rev/s.
(b) ![1561 m/s^2](https://tex.z-dn.net/?f=1561%20m%2Fs%5E2)
The centripetal acceleration of the ball is given by
![a=\frac{v^2}{r}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bv%5E2%7D%7Br%7D)
where
v is the speed
r is the distance of the ball from the centre of the trajectory
For situation 1),
v = 30.6 m/s
r = 0.600 m
So the centripetal acceleration is
![a=\frac{(30.6 m/s)^2}{0.600 m}=1561 m/s^2](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B%2830.6%20m%2Fs%29%5E2%7D%7B0.600%20m%7D%3D1561%20m%2Fs%5E2)
(c) ![1292 m/s^2](https://tex.z-dn.net/?f=1292%20m%2Fs%5E2)
For situation 2 we have
v = 34.1 m/s
r = 0.900 m
So the centripetal acceleration is
![a=\frac{v^2}{r}=\frac{(34.1 m/s)^2}{0.900 m}=1292 m/s^2](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bv%5E2%7D%7Br%7D%3D%5Cfrac%7B%2834.1%20m%2Fs%29%5E2%7D%7B0.900%20m%7D%3D1292%20m%2Fs%5E2)
You would need to ear defenders (I'm assuming these are ear protectors for use with loud sounds) while firing at a gun range. You could use it for loud construction areas.
The wires is what is needed to put together the whole thing, kinda like glue when you're gluing a piece of paper on it.
Anyways, the battery is the main source and main energy per say.
That energy that comes from the battery, thanks to the wires, it can transfer that said energy to both the switch and light bulb.
And as you flick the switch, it depends of how you put it together, there's two options, turning the light bulb on or turning it off.
Though it doesn't mean that since the light bulb is connected to the battery makes the bulb turn on no matter what since the switch can cancel the main source's energy.
- Ouma :>
In solids, particles or atom are very closely arranged compared to gasses. When these particles are arranged in such proximity, vibrations from sound are very easily transmitted from one particle to another in the solid. Hence, the sound vibrations can travel through the solid medium more quickly than through a gas medium.
Speed of sound also depends on its frequency and the wavelength.
To find the ratio of planetary speeds Va/Vb we need the orbital velocity formula:
V=√({G*M}/R), where G is the gravitational constant, M is the mass of the distant star and R is the distance of the planet from the star it is orbiting.
So Va/Vb=[√( {G*M}/Ra) ] / [√( {G*M}/Rb) ], in our case Ra = 7.8*Rb
Va/Vb=[ √( {G*M}/{7.8*Rb} ) ] / [√( {G*M}/Rb )], we put everything under one square root by the rule: (√a) / (√b) = √(a/b)
Va/Vb=√ [ { (G*M)/(7.8*Rb) } / { (G*M)/(Rb) } ], when we cancel out G, M and Rb we get:
Va/Vb=√(1/7.8)/(1/1)=√(1/7.8)=0.358 so the ratio of Va/Vb = 0.358.