A 2100 kg car rounds a curve of 67 m banked at an angle of 13. If the car is traveling at 105 km/h, will a friction force be required? If so, in what direction?
jhk
The frictional force should be directed towards the centre of the curve
To determine if a friction force will be required for the car to successfully make the turn, we can analyze the forces acting on the car. Let's break it down step by step:
1. Determine the gravitational force acting on the car:
The gravitational force (Fg) can be calculated using the formula: Fg = mass * acceleration due to gravity. Given that the mass of the car is 2100 kg and acceleration due to gravity is roughly 9.8 m/s², we can calculate the gravitational force.
Fg = (2100 kg) * (9.8 m/s²) = 20580 N
2. Determine the normal force acting on the car:
The normal force (Fn) is the perpendicular force exerted by a surface to support the weight of an object resting on it. In this case, it acts vertically upwards and is equal in magnitude to the gravitational force.
Fn = 20580 N
3. Analyze the forces acting horizontally on the car:
The horizontal forces are the centripetal force (Fc) and the friction force (Ff). Since the car is driving along a banked curve, the vertical component of the normal force will provide the centripetal force.
Fc = Fn * sin(θ)
Fc = (20580 N) * sin(13°) = 4503 N
4. Compare the required centripetal force to the maximum frictional force:
If the required centripetal force is greater than the maximum frictional force, a friction force will be required to help the car make the turn. Otherwise, the car can make the turn without a friction force.
Since the problem doesn't provide any information about the friction coefficient or the maximum static friction that the tires can provide, we cannot directly determine if a friction force will be required.
It's essential to know the friction coefficient or the maximum static friction available to determine the need for a friction force and its direction. Without that information, we cannot conclusively determine if a friction force is required or its direction.