Question

A car of mass 1250 kg drives around a curve with a speed of 22 m/s.

Answer 1

Answer:

A) About 13.83 m/s²

B) 30.25 m.

Explanation:

Part A)

Centripetal acceleration is given by:

$\displaystyle a_c = \frac{v^2}{r}$

Hence, the centripetal acceleration of the car is:

$\displaystyle a_c = \frac{(22\text{ m/s})^2}{35\text{ m}} \approx 13.83\text{ m/s ^2 }$

Part B)

The force of friction supplies the centripetal force:

$\displaystyle F_f = \frac{mv^2}{r}$

Because the maximum friction that can be supplied is 20,000 N, we have that:

$\displaystyle \frac{mv^2}{r} \leq 20000\text{ N}$

Therefore:

$\displaystyle \begin{aligned} (1250\text{ kg})(22\text{ m/s})^2} & \leq 20000\text{ N}\cdot r \\ \\ r & \geq \frac{(1250\text{ kg})(22\text{ m/s})^2}{20000\text{ N}} \\ \\ r & \geq 30.25\text{ m} \end{aligned}$

The radius of the smallest circle the car can drive is hence 30.25 m.