Question

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

Answer 1

Given

Mass of the car, m=1250 kg

Speed of the car, v=22 m/s

To find

a. Centripetal acceleration of the car

b. The radius of the smallest circle.

Explanation

a. Given the radius is r=35 m

The centripetal acceleration is given by

$\begin{gathered} a=\frac{v^2}{r} \\ \Rightarrow a=\frac{22^2}{35} \\ \Rightarrow a=13.82\text{ m/s}^2 \end{gathered}$

b. The frictional force is F=20,000N

The speed is v=22 m/s

Thus,

$\begin{gathered} F=m\frac{v^2}{r} \\ \Rightarrow20,000=1250\times\frac{22^2}{r} \\ \Rightarrow r=30.25\text{ m} \end{gathered}$

Conclusion

a. The centripetal acceleration is

$13.82\text{ m/s}^2$

b.The radius is 30.25 m