Finding the Normal Force of a block on an incline experiencing centripetal force

In summary, when sliding along a horizontal circular path on the inside of a friction-free cone, the magnitude of the normal force may be greater than mg. This is due to the application of centripetal force, resulting in more force pushing back and potentially resulting in a greater normal force. This can be analyzed by considering forces in the vertical direction and using Newton's 2nd law.
  • #1
trivk96
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Homework Statement


When the sliding along a horizontal circular path on the inside of a friction-free cone, the magnitude of the normal force (use the diagram)

1. is greater than mg, always.
2. is equal to mg.
3. may be greater than mg.
4. is less than mg, always.
5. may be less than mg.

Homework Equations


??

The Attempt at a Solution



I think it is 3 because with centripetal force, more force is being applied to the cone resulting in more force pushing back which means a greater normal force which may be more than mg. Is this correct??
 

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  • #2
Hint: Analyze forces in the vertical direction and apply Newton's 2nd law.
 

1. What is the normal force?

The normal force is the force exerted by a surface on an object in contact with it. It is always perpendicular to the surface and acts to prevent the object from passing through the surface.

2. How is the normal force related to centripetal force?

In the context of a block on an incline experiencing centripetal force, the normal force is equal in magnitude to the component of the object's weight that is perpendicular to the surface of the incline. This normal force is necessary for the object to maintain its circular motion and stay on the incline.

3. How do you calculate the normal force on an incline?

The normal force can be calculated using the formula FN = mg cosθ, where m is the mass of the object, g is the acceleration due to gravity, and θ is the angle of the incline.

4. What happens to the normal force if the angle of the incline changes?

If the angle of the incline changes, the normal force will also change. As the angle increases, the normal force will decrease, and as the angle decreases, the normal force will increase.

5. Why is the normal force important in this scenario?

The normal force is important because it is necessary for the object to maintain its circular motion on the incline. Without the normal force, the object would not have the necessary centripetal force to stay on the incline and would either slide down or off the incline.

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