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.

Step-by-step explanation

a. Given the radius is r=35 m

The centripetal acceleration is given by

`\begin{gathered} a=(v^2)/(r) \\ \Rightarrow a=(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(v^2)/(r) \\ \Rightarrow20,000=1250*(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