Question

A car with a mass of 1000 kg travels around a banked curve with a constant speed of 27 m/s. The radius of curvature of the curve

is 40 m. The magnitude of the horizontal component of the normal force that would be required to produce this centripetal acceleration
in the absence of any friction is__N

Answer 1

The magnitude of the horizontal component of the normal force required is 18225 N.

To calculate the magnitude of the horizontal component of the normal force required to produce the centripetal acceleration in the absence of any friction, we can use the following formula:

Horizontal component of the normal force (N_horizontal) = (m * v^2) / r

where:

m = mass of the car (1000 kg)

v = speed of the car (27 m/s)

r = radius of curvature (40 m)

Now, plug the values into the formula:

N_horizontal = (1000 kg * (27 m/s)^2) / 40 m

N_horizontal = (1000 kg * 729 m^2/s^2) / 40 m

N_horizontal = 729000 kg m^2/s^2 / 40 m

Now, let's convert kg m^2/s^2 to Newtons (N):

1 N = 1 kg m/s^2

N_horizontal = 729000 N / 40

N_horizontal = 18225 N

So, the magnitude of the horizontal component of the normal force required is 18225 N.