Answer:
Centripetal acceleration = 46.26m/s2
Tension = 4.6N
Explanation:
Centripetal acceleration is given by the following formula: [tex]a_c = \frac{v^2}{r}[/tex]
So, to calculate acceleration we first need velocity and radius.
The radius is given to us as 75cm = 0.75m, and we can find velocity from the following formula:[tex]v=r\omega[/tex] where w = the angular velocity given by: [tex]\omega = \frac{2\pi}{T}[/tex]
We are given a period of 0.80s, meaning that our angular velocity is:
[tex]\frac{2\pi}{0.80} = 7.85 rad s^{-1}[/tex]
Now we just need to multiply is by the radius to find the velocity:
[tex]0.75*7.85=5.89ms^{-1}[/tex]
Finally we square the velocity and divide by the radius to find the final centripetal acceleration: [tex]\frac{5.89^{2} }{0.75} =46.26ms^{-2}[/tex]
[tex]F=\frac{mv^{2} }{r}[/tex] so we just need to multiply the centripetal acceleration by mass to get the tension force of the string: [tex]46.26*0.1 = 4.6N[/tex]
Hope this helped!
