A 1400 kg car rounds a curve of 57 m banked at an angle of 14 degree

If the car is traveling at 98 km/h, how much friction force will be required?

I cannot figure out how to solve this problem. Someone please help me?

ΣFy = N• cos θ − mg − f •sin θ = 0

ΣFx = N• sin θ + f •cos θ = m•v²/R,
where f –friction force

Solving the 1st equation for N, we obtain
N =( f •sin θ + m•g)/cos θ,
Substitute N to the 2nd equation and obtain friction force
f =m[(v²•cosθ/R) - g•sinθ].
f=1400[27²•cos14/57 – 9.8•sin18} =
=1400[12.4-2.04] =14000 N

To solve this problem, we need to consider the forces acting on the car as it goes around the banked curve. The main forces involved are the gravitational force, the normal force, and the frictional force.

Let's break down the problem step by step:

1. Identify the relevant variables:
- Mass of the car (m) = 1400 kg
- Radius of the curve (r) = 57 m
- Angle of banking (θ) = 14 degrees
- Speed of the car (v) = 98 km/h

2. Calculate the speed of the car in meters per second:
Since the speed is given in kilometers per hour, we need to convert it to meters per second. We know that 1 km/h = 0.2778 m/s. So, we can calculate:
Speed (v) = 98 × 0.2778 = 27.2234 m/s (approximately)

3. Determine the centripetal force:
The centripetal force is the force directed toward the center of the circular path that keeps the car moving along the curved track. It is given by the equation:
Centripetal force (Fc) = (m × v^2) / r

Plugging in the values:
Fc = (1400 × 27.2234^2) / 57

4. Find the gravitational force:
The gravitational force acting on the car is given by:
Gravitational force (Fg) = m × g
where g is the acceleration due to gravity (approximately 9.8 m/s^2)

Plugging in the values:
Fg = 1400 × 9.8

5. Calculate the normal force:
The normal force (Fn) is the force exerted by the surface supporting the car. In this case, it acts perpendicular to the inclined plane. It can be found using the equation:
Fn = m × g × cos(θ)
Since the car is on a banked curve, we need to calculate the vertical component of the gravitational force, which is given by mg × cos(θ).

Plugging in the values:
Fn = 1400 × 9.8 × cos(14)

6. Determine the frictional force:
The frictional force (Ff) is the force acting parallel to the inclined plane, opposing the motion of the car. Since the car is on a banked curve and is not sliding, the frictional force is not required to keep the car from sliding down the curve. It only needs to provide the necessary centripetal force. Therefore, the frictional force is zero.

In conclusion, no friction force is required to keep the car moving around the banked curve.