## Centripetal Force

Consider a car is traveling 30 m/s on a road with lots of pot holes, and sharply turns to narrowly miss one. If the vehicle’s path is a 150 m curve radius and the force produced by its tires is 1,000 N, what is the car’s weight?

##
__
__**Hint**

**Hint**

Centripetal acceleration:

$$$a=\frac{v^2}{r}$$$

where
$$v$$
is the velocity, and
$$r$$
is the radius.

##
__
__**Hint 2**

**Hint 2**

$$$Force=mass\times acceleration$$$

Any motion on a curved path has accelerated motion:

$$$a=\frac{v^2}{r}$$$

where
$$a$$
is centripetal acceleration,
$$v$$
is the velocity, and
$$r$$
is the radius. To stay on the curved path, a force directed towards the curvature’s center is required, and is called centripetal force:

$$$F=ma_{centripetal}=\frac{mv^2}{r}$$$

where
$$m$$
is the mass and
$$a$$
is the acceleration. Therefore,

$$$1,000N=\frac{m(30m/s)^2}{150m}$$$

Solving for mass:

$$$m=\frac{1,000N(150m)}{900m^2/s^2}=\frac{(1,000kg\cdot m)(150m)}{(s^2)(900m^2/s^2)}=167\:kg$$$

167 kg