How much centripetal force is needed to keep a 60.0 person and skate board moving at 6.0 in a circle with a 10.0 m radius?

To calculate the centripetal force required to keep a 60.0 kg person and skateboard moving in a circle, we use the formula ( F_c = \frac{mv^2}{r} ), where ( m ) is the mass (60.0 kg), ( v ) is the velocity (6.0 m/s), and ( r ) is the radius (10.0 m). Plugging in the values:

[ F_c = \frac{60.0 , \text{kg} \times (6.0 , \text{m/s})^2}{10.0 , \text{m}} = \frac{60.0 , \text{kg} \times 36.0 , \text{m}^2/\text{s}^2}{10.0 , \text{m}} = 216.0 , \text{N}. ]

Therefore, a centripetal force of 216.0 N is needed.