Question

2. A 1200 kg car rounds a horizontal curve that is a section of a circle of radius 70 m. If the car is traveling at 18 m/s, findA) the centripetal acceleration of the car andB) the static friction coefficient needed to keep the car from slipping.

Answer 1

a)a= 4.62 m/s²

b)μ = 0.462

Step-by-step explanation:

Given that

m= 1200 kg

r = 70 m

v= 18 m/s

a)

Centripetal acceleration ,a

`a=(v^2)/(r)`

By putting the values

`a=(v^2)/(r)`

`a=(18^2)/(70)\ m/s^2`

a= 4.62 m/s²

b)

To keep the car from slipping ,the radial force should be equal to the friction force

`Fr=m(v^2)/(r)`

`\mu mg=m(v^2)/(r)`

`\mu =(v^2)/(rg)`

By putting the values

`\mu =(v^2)/(rg)`

`\mu =(18^2)/(70* 10)` ( take g =10 m/s²)

μ = 0.462