Question

A stone is whirled at the end of a rope 25m long makes 8 complete revolution in two seconds find its centripetal force and centripetal acceleration. Pls if it is correct i promise.
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Answer 1

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)

$F_{c}=m*\frac{v^{2} }{r}$

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

$\frac{8rev}{2s}*\frac{2*\pi *rad}{1 rev} =\frac{25.13rad}{s}$

v = 25.13*25 = 628.31[m/s]

Now replacing in the first equation:

$F_{c}=0.1*\frac{628.31^{2} }{25} \\F_{c}= 1579 [N]$

b)

The second part will be only:

$a_{c}=\frac{v^{2} }{r} \\a_{c}=\frac{628.31^{2} }{25} \\a_{c}=15790.93[m/s^{2} ]$