Question

The force needed to keep a car from skidding on a curve varies jointly as theweight of the car and the square of the car’s speed and inversely as the radiusof the curve. If 126 lb of force keeps a 1200 lb car driving at 25 mph fromskidding on a curve of radius 400 ft, what force would keep the same car going45 mph from skidding on a curve of radius 650 ft?

Answer 1

Answer:

F' = 251.2 lb

Explanation:

It is given that,

The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the car’s speed and inversely as the radius of the curve. So,

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

W is the weight

v is the speed

r is the radius of curve

W is constant, So

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

If F = 126 lb, v = 25 mph and r = 400 ft

F' = ?, v' = 45 mph and r' = 650 ft

$\dfrac{F}{F'}=(\dfrac{v}{v'})^2\times (\dfrac{r'}{r})$

$\dfrac{126}{F'}=(\dfrac{25}{45})^2\times (\dfrac{650}{400})$

On solving above equation,

F' = 251.2 lb

So, 251.2 lb of force would keep the same car going 45 mph from skidding on a curve of radius 650 ft. Hence, this is the required solution.