Sara and Meg are on a merry-go-round Sara is sitting closer to the outside of the merry-go-round (radius=5m) while Meg chose a horse on the inside of the ride (radius=3m) Both girls have the same mass of 80 kg.Sara's tangential velocity is 3.4m/s and Meg's tangential velocity is 2.1m/s Which girl has the larger centripetal force? Sara They are equal. Meg Not enough information to determine.

## Step 1<br />The problem involves the concept of centripetal force, which is the force that keeps an object moving in a circular path. The centripetal force is given by:<br />### \(F = \frac{mv^2}{r}\)<br />where \(F\) is the centripetal force, \(m\) is the mass of the object, \(v\) is the velocity of the object, and \(r\) is the radius of the circular path.<br /><br />## Step 2<br />In this problem, both Sara and Meg have the same mass (\(m = 80kg\)), but different velocities (\(v = 3.4m/s\) for Sara and \(v = 2.1m/s\) for Meg) and different radii (\(r = 5m\) for Sara and \(r = 3m\) for Meg).<br /><br />## Step 3<br />We can calculate the centripetal force for each girl using the formula from Step 1.<br /><br />For Sara, the centripetal force is:<br />### \(F_{Sara} = \frac{80kg \times (3.4m/s)^2}{5m} = 231.2 N\)<br /><br />For Meg, the centripetal force is:<br />### \(F_{Meg} = \frac{80kg \times (2.1m/s)^2}{3m} = 56.8 N\)<br /><br />## Step 4<br />Comparing the two forces, we can see that Sara's centripetal force is greater than Meg's.