A car of mass 1600 kg is traveling without slipping on a flat, curved road with a radius of curvature of 38 m. If the car's speed is 15 m/s, what is the frictional force between the road and the tires? in Newtons

To find the frictional force between the road and the car's tires, we need to first determine the net inward force acting on the car. In this case, the net inward force is provided by the frictional force.

To begin, let's calculate the car's acceleration using the equation for centripetal acceleration:

a = v^2 / r

where
a is the centripetal acceleration,
v is the velocity, and
r is the radius of curvature.

Plugging in the given values, we get:

a = (15 m/s)^2 / 38 m

Simplifying, we find:

a = 5.921 m/s^2

Now, we can find the net inward force using Newton's second law of motion:

F_net = m * a

where
F_net is the net inward force,
m is the mass of the car, and
a is the acceleration.

Plugging in the given values, we have:

F_net = (1600 kg) * (5.921 m/s^2)

Simplifying, the net inward force is:

F_net = 9473.6 N

Therefore, the frictional force between the road and the tires is 9473.6 N.