How do you find centripetal force without knowing velocity?

In summary: The radial component is the centripetal force needed to keep the ball moving in a circle. In summary, the problem is asking for the centripetal force acting on a tetherball going around a pole at a constant velocity. The rope has a length of 2 meters and makes a 30 degree angle below the horizon, and the ball has a mass of 0.5 kg. The relevant equations are F(gravity) = m*a and F(centripetal) = mv^2/r. By drawing a force diagram and resolving forces, the centripetal force can be determined.
  • #1
annamarie424
1
0

Homework Statement



A tetherball goes around the pole at a constant velocity. The rope has a 2m length, makes a 30 degree angle below the horizon and the ball's mass is .5 kg.

Homework Equations



F(gravity)=m*a

F(centripetal)=mv^2/r

The Attempt at a Solution


I'm stuck at trying to find centripetal force.
 
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  • #2
annamarie424 said:

Homework Statement



A tetherball goes around the pole at a constant velocity. The rope has a 2m length, makes a 30 degree angle below the horizon and the ball's mass is .5 kg.

Homework Equations



F(gravity)=m*a

F(centripetal)=mv^2/r

The Attempt at a Solution


I'm stuck at trying to find centripetal force.
Hello annamarie424. Welcome to PF !

Find it from the centripetal force, which is the component of the force producing the circular motion.
 
  • #3
Hi annamarie424 - Draw a force diagram showing the pole vertically with the ball and string making a 30 degree angle. Draw on the forces acting on the ball. In this view the ball isn't moving (eg it's not falling down, nor is it rising up) so some of the forces are in balance (eg they sum to zero).

If you are still stuck try putting your diagram on an image hosting site and providing a link. Once you have made 10 (?) posts on this forum you can upload images directly.
 
  • #4
Note it's not really a tetherball, the rope is not winding around the pole, instead the rope is attached to a frictionless pivot and the length (2 m) and angle (30 °) remain constant.
 
  • #5
centripetal force in this case is just the net radial force. Take some tension T in the rope and resolve the components of the weight in radial and tangential directions.
 

1. How is centripetal force calculated without knowing velocity?

Centripetal force can be calculated using the equation F = m * a, where m is the mass of the object and a is the acceleration towards the center of the circle. This acceleration can be found using the formula a = v^2 / r, where v is the velocity and r is the radius of the circle. Therefore, if the velocity is unknown, the acceleration can still be calculated using the radius of the circle.

2. Can centripetal force be found using only the radius and mass of an object?

Yes, as mentioned before, the centripetal force can be calculated using the formula F = m * a. The acceleration, which is necessary to calculate the force, can be found using the radius and mass of the object.

3. Is the centripetal force always directed towards the center of the circle?

Yes, centripetal force is always directed towards the center of the circle. This is because it is the force that keeps an object moving in a circular path, and in order for an object to move in a circular path, it must constantly be pulled towards the center.

4. Can centripetal force be negative?

No, centripetal force cannot be negative. Since it is a force that is directed towards the center of the circle, it is always positive. However, the direction of the force can change depending on the direction of the object's motion.

5. How does changing the velocity affect the centripetal force?

Changing the velocity of an object will also change the centripetal force acting on it. This is because the acceleration towards the center of the circle is directly proportional to the square of the velocity. Therefore, increasing the velocity will increase the acceleration and the force needed to keep the object moving in a circular path.

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