Question

An SUV has a mass of 6000 kg and a compact car has a mass of 2000 kg. They both go around the same unbanked circular curve on the freeway. Bumper to bumper they go with the same speed vo. The centripetal acceleration of the compact car is ao and the centripetal force acting is Fo. The centripetal acceleration of the SUV is _____ ao of the compact car.

Answer 1

Answer:

Therefore, the centripetal acceleration of the SUV is 3 times ao of the compact car.

Explanation:

FOR SUV:

$ac_{suv} = \frac{mv^2}{r}$

where,

ac_suv = centripetal acceleration of the SUV = ?

m = mass of SUV = 6000 kg

v = speed of SUV = vo

r = radius of path

Therefore,

$ac_{suv} = \frac{6000\ vo^2}{r}$---------------- equation (1)

FOR CAR:

$ao = \frac{mv^2}{r}$

where,

ao = centripetal acceleration of the car = ?

m = mass of car = 2000 kg

v = speed of car = vo

r = radius of path

Therefore,

$ao = \frac{2000\ vo^2}{r}$--------------------- equation (2)

Dividing equation (1) by eq(2):

$\frac{ac_{suv}}{ao} = \frac{6000}{2000}\\\\ac_{surv} = 3ao$

Therefore, the centripetal acceleration of the SUV is 3 times ao of the compact car.