How can gravity be greater than the centripetal force?

In summary, the highlighted sentence in the physics textbook states that it is possible for the weight to be greater than the centripetal force when the car is at the top of the circle. This is because the weight and the reaction (normal) force can be either lower or higher than the centripetal force, but only when they are exactly equal will the car follow a circular path. The normal force is the sum of the centripetal force and the weight, and if at the top the weight is greater than the required value of centripetal force, then the car will follow a different trajectory and detach from the track. The sum of all forces being equal to the centripetal force is the condition for circular motion, and if
  • #1
Naser Tay
So I saw this in my physics textbook and according to the highlighted sentence, it is possible for the weight to be greater than the centripetal force when the car is at the top of the circle. But how is this possible when the weight itself is PART of the centripetal force when the car is at the top?
 

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  • #2
Naser Tay said:
But how is this possible when the weight itself is PART of the centripetal force when the car is at the top?
The weight is not part of the centripetal force. I don't really like the diagram because it shows normal force instead of centripetal force. Normal force is the sum of centripetal force and weight, so why not just show the two components separately? It looks confusing to me.
 
  • #3
Naser Tay said:
So I saw this in my physics textbook and according to the highlighted sentence, it is possible for the weight to be greater than the centripetal force when the car is at the top of the circle. But how is this possible when the weight itself is PART of the centripetal force when the car is at the top?
Centripetal force is just some value the sum of all actual forces must have in order to make something go in circles.
These forces here are the weight and the reaction (normal) force. They can be lower or higher than the centripetal force, but only if they together are exactly equal to it will the car follow a circular path.
So, if weight at the top is larger than the required value of centripetal force, then so is the sum of weight and reaction force, and the car will follow a different trajectory than circular (=it will detach from the track and fall).

Once again, the sum of all forces being equal to centripetal force is the condition for circular motion. If these forces don't meet this condition, then there's no circular motion.

russ_watters said:
Normal force is the sum of centripetal force and weight
Is it? At the top you'd have ##W+F_c=R_t##. At the Bottom you'd have ##W-F_c=R_b## And yet, ##R_t<R_b##.
 

1. How can gravity be greater than the centripetal force?

Gravity is a fundamental force that exists between any two objects with mass. It is the force that causes objects to be attracted towards each other. On the other hand, centripetal force is the force that keeps an object moving in a circular path. In some cases, the force of gravity can be greater than the centripetal force, causing the object to change its path or fall towards the center of rotation.

2. What is the relationship between gravity and centripetal force?

The relationship between gravity and centripetal force is based on Newton's laws of motion. According to the second law, the force required to keep an object moving in a circular path is directly proportional to the mass of the object and the square of its velocity. On the other hand, the force of gravity is dependent on the mass of the objects and the distance between them. Therefore, the strength of gravity can be greater than the centripetal force in certain situations.

3. Can the centripetal force ever be greater than gravity?

Yes, it is possible for the centripetal force to be greater than the force of gravity. This can happen when the object is moving at a high velocity or when the distance between the objects is significant. In such cases, the centripetal force must be strong enough to balance the gravitational force and keep the object in its circular path.

4. What factors affect the strength of gravity and centripetal force?

The strength of gravity is affected by the masses of the objects and the distance between them. The larger the mass of the objects or the smaller the distance between them, the stronger the force of gravity will be. On the other hand, the strength of the centripetal force is affected by the mass of the object, its velocity, and the radius of its circular path. A larger mass or higher velocity will require a stronger centripetal force, while a smaller radius will result in a stronger force.

5. Why is it important to understand the relationship between gravity and centripetal force?

Understanding the relationship between gravity and centripetal force is essential in many fields of science, such as astronomy, physics, and engineering. It helps explain the motion of celestial bodies, the behavior of objects in orbit, and the design of structures like roller coasters and satellites. It is also crucial for predicting and understanding the effects of gravity on objects in our daily lives.

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