For this problem, assume that the acceleration due to gravity, g, is 10 m/s². A Mazda Miata is traveling at 90.0 km/h around a curve whose radius is 475 m. The mass of the Miata plus driver and passenger is 1350 kg. Assuming that the acceleration of gravity is 10.0 m/s², the centripetal force required to maintain the car around the curve is A) 1.49 $\times$ 10³ N. B) 1.78 $\times$ 10³ N. C) 1.81 $\times$ 10³ N. D) 1.86 $\times$ 10³ N.

Question

Quizplus · Accepted Answer

The centripetal force $F_c$ required to maintain the car on a curve is given by the formula $F_c = \frac{mv^2}{r}$, where $m$ is the mass of the car, $v$ is the velocity of the car, and $r$ is the radius of the curve. First, convert the speed from km/h to m/s: $90.0 \, \text{km/h} = 90.0 \times \frac{1000 \, \text{m}}{3600 \, \text{s}} = 25 \, \text{m/s}$. Then, substitute the given values into the formula: $F_c = \frac{1350 \times (25)^2}{475} = 1.78 \times 10^3 \, \text{N}$.

For This Problem, Assume That the Acceleration Due to Gravity ×\times×

For This Problem, Assume That the Acceleration Due to Gravity $\times$