Question

Car 1 goes around a level curve at a constant speed of 65 km/h . The curve is a circular arc with a radius of 95 m . Car 2 goes around a different level curve at twice the speed of Car 1. How much larger will the radius of the curve that Car 2 travels on have to be in order for both cars to have the same centripetal acceleration

Answer 1

For Car 2 to have the same centripetal acceleration while traveling at twice the speed of Car 1, it must travel on a curve with a radius that is four times larger, which would be 380 meters.

Step-by-step explanation:

The centripetal acceleration (ac) of a car going around a level curve at a constant speed is given by the formula ac = v2 / r, where v is the speed of the car and r is the radius of the circular path. If Car 1 is traveling at 65 km/h and has a centripetal acceleration on a curve with a radius of 95 m, and Car 2 is traveling at twice the speed of Car 1, we are asked to find the required radius of the curve for Car 2 to maintain the same centripetal acceleration.

To keep the same centripetal acceleration for Car 2, which is moving at twice the speed, the radius r2 must be increased proportionally to the square of the speed ratio. Since Car 2 is traveling at twice the speed, the radius must be increased by a factor of 22, or 4 times larger than that for Car 1. Therefore, if Car 1's radius is 95 m, Car 2's radius needs to be 95 m * 4, which is 380 m.

Answer 2

The radius of the curve that Car 2 travels on is 380 meters.

Step-by-step explanation:

Speed of car 1,
`v_1=65\ km/h`

Radius of the circular arc,
`r_1=95\ m`

Car 2 has twice the speed of Car 1,
`v_2=130\ km/h`

We need to find the radius of the curve that Car 2 travels on have to be in order for both cars to have the same centripetal acceleration. We know that the centripetal acceleration is given by :

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

According to given condition,

`(v_1^2)/(r_1)=(v_2^2)/(r_2)`

`(65^2)/(95)=(130^2)/(r_2)`

On solving we get :

`r_2=380\ m`

So, the radius of the curve that Car 2 travels on is 380 meters. Hence, this is the required solution.