Answer:
v=1.5081 m/s
[tex]F_c=0,189\ Nw[/tex]
Explanation:
Uniform Circular Motion
The cork is performing a circular motion which we assume to be uniform (constant angular speed or angular acceleration zero)
The centripetal force applied to it is given by
[tex]F_c=m\ a_c[/tex]
where m is the mass and [tex]a_c[/tex] is the centripetal acceleration. This acceleration appears since the tangent speed is constantly changing direction. If w is the angular speed and r is the radius of rotation
[tex]a_c=w^2r[/tex]
The speed of the cork can be found with the formula
[tex]v=wr[/tex]
We can compute w since we know the rotation period T=1.25 sec
[tex]w=\frac{2\pi}{T}=\frac{2\pi}{1.25}=5.027\ rad/sec[/tex]
Now, since r=0.30 m, let's compute v
[tex]v=wr=(5.027)(0.3)=1.5081\ m/s[/tex]
[tex]a_c=5.027^2(0.3)=7.58\ m/sec^2[/tex]
And finally
[tex]F_c=(0.025)\ (7.58)=0,189\ Nw[/tex]
