Circular Motion Problem: Finding Speed of a Swinging Ball at a Given Angle

In summary: But the ball will be travelling in a circle, so the net force must be towards the centre of the circle. Resolve the net force into components parallel and perpendicular to the string. In summary, to determine the speed of the ball at the given instant, you must add the weight force and tension force, resolve the net force into components parallel and perpendicular to the string, and use the equation T-mgcos30°=m(v2/r) to solve for the velocity. It is important to draw a free body diagram and ensure that all force components are added correctly.
  • #1
bcd201115
20
0

Homework Statement


a .30kg ball attached to the end of a string swings in a vertical circle having a radius of 1.4m. At the instant when the string makes an angle of 30° above the horizontal, the tension in the string is 3N. What is the speed of the ball at this instant?


Homework Equations


Can anyone help me with this one?


The Attempt at a Solution


T-mgcos30°=m(v2/r)
then solve for velocity? Am i doing this right?
 
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  • #2
bcd201115 said:

Homework Statement


a .30kg ball attached to the end of a string swings in a vertical circle having a radius of 1.4m. At the instant when the string makes an angle of 30° above the horizontal, the tension in the string is 3N. What is the speed of the ball at this instant?

Homework Equations


Can anyone help me with this one?

The Attempt at a Solution


T-mgcos30°=m(v2/r)
then solve for velocity? Am i doing this right?
Red mine.

Almost right. Draw a free body diagram to ensure your force components are being added correctly. :wink:

[Edit: I highlighted something else in red. See PeterO's response below. He gives some good advice here. But it looks to me like you were originally on the right track by summing all of the force components in the radial direction (parallel to the string). You just need to make sure the components are correct and that you are adding up in the right direction. (Again, a FBD might help this process.)]
 
Last edited:
  • #3
bcd201115 said:

Homework Statement


a .30kg ball attached to the end of a string swings in a vertical circle having a radius of 1.4m. At the instant when the string makes an angle of 30° above the horizontal, the tension in the string is 3N. What is the speed of the ball at this instant?


Homework Equations


Can anyone help me with this one?


The Attempt at a Solution


T-mgcos30°=m(v2/r)
then solve for velocity? Am i doing this right?

I don't think it is as simple as that.

I would be adding the weight force (down) to the Tension (along the string - you can only pull with a string)

This will give a net force angled down from the string.

Resolve that force parallel and perpendicular to the string.

The component parallel to the string represents the centripetal force.

The component perpendicular to the string represents the force slowing the ball - remember the ball will slow as it rises through the circle, and speed up as descends again.

Note: the string makes an angle of 30o above the horizontal, so the tension in the string is at 30o below the horizontal. Once the force of gravity is added to that, the net force will be at, perhaps 60o below the horizontal.
 

What is circular motion?

Circular motion refers to the movement of an object along a circular path, where the distance from the center remains constant. This type of motion can occur both in a horizontal plane, like a car driving around a roundabout, or in a vertical plane, like a rollercoaster moving in a loop.

What causes circular motion?

Circular motion is caused by a centripetal force, which is directed towards the center of the circular path. This force is required to keep an object moving along a circular path, as without it, the object would move in a straight line tangent to the circle.

How is circular motion related to rotational motion?

Circular motion is a type of rotational motion, where an object rotates around an axis. The axis of rotation in circular motion is the center of the circle, and the object's tangential speed is related to its angular velocity.

What is the difference between uniform and non-uniform circular motion?

Uniform circular motion refers to a circular path where the object moves at a constant speed, while non-uniform circular motion refers to a circular path where the object's speed changes. In non-uniform circular motion, the centripetal force may also vary, causing the object to move in a non-uniform manner.

How is circular motion used in real-world applications?

Circular motion has many real-world applications, such as in amusement park rides, satellite orbits, and the motion of planets around the sun. It is also used in everyday activities, such as driving a car around a curve or swinging a ball attached to a string in a circular motion. Engineers also use circular motion to design machinery, such as engines or turbines, that require rotational motion to function.

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