Question

A 2000 kg car rounds a circular turn of radius 20 m. If

theroad is flat and the coefficient of friction between tires and
roadis 0.70, how fast can the car go without skidding?

Answer 1

car can move at 11 m/s without skidding.

Step-by-step explanation:

given,

mass of car = 2000 kg

radius of turn = 20 m

μ = 0.7

using centripetal force

F =
`(mV^2)/(R)`.....................(1)

and we know

F = μ N = μ m g........................(2)

equating both the equation (1) and (2)

μ m g =
`(mV^2)/(R)`

v =
`√(\mu R g)`

v =
`√(0.7 * 20 * 9.81)`

v = 11.71 m/s

hence, car can move at 11 m/s without skidding.

Answer 2

The velocity of car is 11.71 m/s.

Step-by-step explanation:

Given that,

Mass of car = 2000 kg

Radius = 20 m

Coefficient of friction = 0.70

We need to calculate the velocity of car

Using relation centripetal force and frictional force

`F= (mv^2)/(r)`...(I)

`F=\mu mg`...(II)

From equation (I) and (II)

`(mv^2)/(r)=\mu mg`

`v=√(\mu* r* g)`

Put the value into the formula

`v=√(0.70*20*9.8)`

`v=11.71\ m/s`

Hence, The velocity of car is 11.71 m/s.