What is the tension in the string at the top of the ball's path?

In summary, a ball of mass 0.300 kg with a speed of 4.00 m/s is revolving at a uniform rate in a vertical circle with a radius of 60.0 cm. The tension in the string when the ball is at the top of its path can be calculated using the equation Ft = ((mv^2)/r)) + mg, resulting in a tension of 5.06 N when the correct value for mg (2.94 N) is used.
  • #1
Toxage
17
0

Homework Statement



Picture: http://img151.imageshack.us/img151/9393/physicszn8.jpg

A ball on the end of a string is cleverly revolved at a uniform rate in a vertical circle of radius 60.0 cm, as shown in Fig. 5-33. Its speed is 4.00 m/s and its mass is 0.300 kg.

(a) Calculate the tension in the string when the ball is at the top of its path.


Homework Equations



EF = ma


The Attempt at a Solution



EF = ma
Ft + Fg = ma
Ft = mac - Fg

Ft = ((mv^2)/r)) + mg
Ft = 8 - 5.88
Ft = 2.12

This answer is incorrect.
 
Last edited by a moderator:
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  • #2
Recalculate mg.

;)
 
  • #3
thejinx0r said:
Recalculate mg.

;)

Wow, I made a huge mistake... I had .6m * 9.8m/s^2 for mg... lol

New MG

0.300kg * 9.8m/sec^2 = 2.94.

8 - 2.94 = 5.06 N.
 

FAQ: What is the tension in the string at the top of the ball's path?

What is vertical circular motion?

Vertical circular motion is the movement of an object in a circular path that is perpendicular to the ground. This means that the object's path is constantly changing direction in a vertical plane.

What causes an object to move in vertical circular motion?

An object moves in vertical circular motion due to the presence of a centripetal force, which is directed towards the center of the circular path. This force is necessary to keep the object moving in a circular path rather than in a straight line.

How is the speed of an object in vertical circular motion related to its radius?

The speed of an object in vertical circular motion is inversely proportional to its radius. This means that as the radius increases, the speed of the object decreases, and vice versa. This relationship is described by the equation v = √(gR), where v is the speed, g is the acceleration due to gravity, and R is the radius of the circular path.

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

Uniform vertical circular motion is when the speed of the object remains constant throughout the circular path. Non-uniform vertical circular motion is when the speed of the object changes at different points along the circular path. In non-uniform motion, the object may experience acceleration or deceleration as it moves along the path.

How is vertical circular motion related to centripetal acceleration?

Centripetal acceleration is the acceleration experienced by an object in circular motion due to the centripetal force. In vertical circular motion, the direction of centripetal acceleration changes as the object moves along the circular path, always pointing towards the center of the circle. The magnitude of centripetal acceleration is given by the equation a = v²/R, where a is the acceleration, v is the speed, and R is the radius of the circular path.

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