Question

A curve in a road forms part of a horizontal circle. As a car goes around it at constant speed 14.0 m/s, the total horizontal force on the driver has magnitude 130 N. What is the total horizontal force on the driver if the speed on the same curve is 18.0 m/s instead?

Answer 1

Explanation:

It is given that,

Initial speed, v₁ = 14 m/s

Initial force, F₁ = 130 N

We need to find the total horizontal force (F₂) on the driver if the speed on the same curve is 18.0 m/s instead, v₂ = 18 m/s

The centripetal force is given by :

$F=\dfrac{mv^2}{r}$

$\dfrac{F_1}{F_2}=\dfrac{mv_1^2/r}{mv_2^2/r}$

$\dfrac{F_1}{F_2}=\dfrac{v_1^2}{v_2^2}$

$F_2=\dfrac{v_2^2\times F_1}{v_1^2}$

$F_2=\dfrac{(18\ m/s)^2\times 130\ N}{(14\ m/s)^2}$

$F_2=214.8\ N$

So, if the speed is 18 m/s, then the horizontal force acting on the car is 214.8 N. Hence, this is the required solution.