# How Does the Normal Force Compare to the Car's Weight in a Circular Valley?

• courtney1121
In summary, the normal force is the force exerted by a surface on an object, while weight is the force of gravity acting on an object. The magnitude of the normal force is determined by the weight of the object and the angle of the surface, and it can never be greater than the weight. The normal force always acts in the opposite direction of weight and can affect the motion of an object by either supporting it or limiting its motion.
courtney1121
A car travels at a constant speed of 23 m/s through a small valley whose cross section is like a circule of radius 310 m. What is the magnitude of the normal force on the car, expressed as a multiple of the car's weight?

what does it mean by the cross section and how does it relate to the problem?

You can assume the valey is sort of a semi-cylinder and the car travels on the circular part of it.

The cross section refers to the shape of the valley as seen from a bird's eye view. In this case, it is a circular shape with a radius of 310 m. This information is relevant because it helps us understand the curvature of the valley and how it may affect the car's motion.

To calculate the magnitude of the normal force on the car, we need to consider the forces acting on the car. The two main forces are the normal force and the weight of the car. The normal force is the force exerted by the surface of the valley on the car, perpendicular to the surface. The weight of the car is the force exerted by gravity on the car, directed towards the center of the Earth.

Since the car is traveling at a constant speed, we can assume that the net force acting on the car is zero. This means that the normal force must be equal in magnitude and opposite in direction to the weight of the car.

Using the formula for centripetal force (F = mv^2/r), we can calculate the magnitude of the centripetal force acting on the car, which is equal to the normal force. We know the mass of the car (m), its speed (v), and the radius of the circle (r).

Once we have calculated the magnitude of the normal force, we can express it as a multiple of the car's weight by dividing it by the weight of the car (mg). This will give us a dimensionless number, as both the normal force and weight are measured in Newtons (N).

In conclusion, the magnitude of the normal force on the car can be calculated using the formula for centripetal force and expressed as a multiple of the car's weight. The cross section of the valley, represented by the circular shape with a radius of 310 m, is important in understanding the forces acting on the car and how they contribute to its motion.

## 1. What is the difference between normal force and weight?

The normal force is the force exerted by a surface on an object that is in contact with it, perpendicular to the surface. Weight is the force of gravity acting on an object, pulling it towards the center of the Earth. While the normal force is a reaction force to the weight, they are two distinct forces that act on an object.

## 2. How is the magnitude of the normal force determined?

The magnitude of the normal force is determined by the weight of the object and the angle of the surface it is in contact with. The normal force is equal in magnitude to the component of the weight that is perpendicular to the surface.

## 3. Can the normal force ever be greater than weight?

No, the normal force can never be greater than the weight of the object. It can only be equal to or less than the weight, depending on the angle of the surface and the weight of the object.

## 4. Does the normal force always act in the opposite direction of weight?

Yes, the normal force always acts in the opposite direction of weight. This is because the normal force is a reaction force to the weight, and Newton's third law states that for every action, there is an equal and opposite reaction.

## 5. How does normal force affect the motion of an object?

The normal force can affect the motion of an object by either supporting it against the force of gravity or by limiting its motion. For example, if an object is on a ramp, the normal force will help keep it from sliding down the ramp. On the other hand, if an object is on a surface with a normal force greater than its weight, it will accelerate upwards.

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