Circular Motion and speed of mass

In summary, to determine the speed of a mass moving in a horizontal circle of radius r inside a frictionless cone of angle 2t, use the equation N = m*v^2/r and take into account the forces of normal force and gravity. Remember that normal force is perpendicular to the surface of the cone and will lead to the net force in the same direction as the acceleration.
  • #1
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A mass m moves in a horizontal circle of radiuss r inside a frictionless cone of angle 2t. Determine the speed of the mass.

I drew the free body diagram for the mass. Normal force points toward the center in the same direction as the acceleration. Gravity points down.

x) N = m*v^2/r

I don't know why, but gravity is the only force acting in the vertical direction. There is nothing to balance it out.

I know that I will need to use the angle 2t somehow, but I don't know what to do.
 
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  • #2
The NET force will point in the same direction as the acceleration (that's from Newton's 2nd law). The normal force will point normal (perpendicular) to the surface of the cone and thus slightly upwards.
 
  • #3
Yes, that's right. Remember by definition normal force is wel, NORMAL to the surface. You should be able to find it easily now. Weight leads to normal, normal leads to net.
 

1. What is circular motion?

Circular motion refers to the movement of an object along a circular path, with a constant distance from a fixed point. This type of motion is characterized by a changing direction but a constant speed.

2. How is circular motion different from linear motion?

Circular motion involves movement along a curved path, while linear motion involves movement along a straight path. In circular motion, the object's velocity is constantly changing due to the changing direction, while in linear motion, the object's velocity remains constant.

3. What factors affect the speed of an object in circular motion?

The speed of an object in circular motion is affected by the radius of the circular path, the mass of the object, and the centripetal force acting on the object. The greater the radius and mass, the faster the object will move, while a greater centripetal force will also increase the speed.

4. How is the speed of an object in circular motion calculated?

The speed of an object in circular motion can be calculated using the formula v = (2πr)/T, where v is the speed, r is the radius of the circular path, and T is the time it takes for the object to complete one full revolution.

5. What is the relationship between speed and centripetal force in circular motion?

The speed of an object in circular motion is directly proportional to the centripetal force acting on the object. This means that as the speed of the object increases, the centripetal force must also increase in order to keep the object moving in a circular path.

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