Answer:
Fc = 1579 [N]; ac = 15790.9 [m/s^2]
Explanation:
To solve this problem we must use the following formula that relates the centripetal force to the speed of rotation and the radius of rotation, respectively.
a)
[tex]F_{c}=m*\frac{v^{2} }{r}[/tex]
where:
Fc = centripetal force [N]
m = mass [kg]
v = tangential velocity [m/s]
r = radius [m]
We have to give a mass to the stone in order to solve the problem, for this case we will say that the mass is equal to 100 [g].
The tangential velocity is equal to the product of the angular velocity (rotational) by the turning radius
v = w * r
But we need to convert the angular velocity units of revolutions per second to radians per second
[tex]\frac{8rev}{2s}*\frac{2*\pi *rad}{1 rev} =\frac{25.13rad}{s}[/tex]
v = 25.13*25 = 628.31[m/s]
Now replacing in the first equation:
[tex]F_{c}=0.1*\frac{628.31^{2} }{25} \\F_{c}= 1579 [N][/tex]
b)
The second part will be only:
[tex]a_{c}=\frac{v^{2} }{r} \\a_{c}=\frac{628.31^{2} }{25} \\a_{c}=15790.93[m/s^{2} ][/tex]
