Answer
Result \[ \|\mathbf{F}\| \approx 257.20 \, \text{N} \]
Work Step by Step
Given speed $10 \, \text{km/h}$ ($\frac{100}{36} \, \text{m/s}$) and force in newtons exerted by the road on a $500 \, \text{kg}$ go-cart driven at a speed of $10 \, \text{km/h}$ around a circular track of radius $15 \, \text{m}$, then \[ \|\mathbf{v}\| = \frac{100}{36} \, \text{m/s} \] \[ \|\mathbf{F}\| = m\kappa\left(\frac{ds}{dt}\right)^2 \] \[ \|\mathbf{F}\| = \frac{500}{15} \cdot \left(\frac{100}{36}\right)^2 \approx 257.20 \, \text{N} \] Result \[ \|\mathbf{F}\| \approx 257.20 \, \text{N} \]
