How Do You Calculate Tension and Speed in Rotating Bead Physics Problems?

In summary, the problem involves a 100 g bead sliding along a string attached to a vertical pole. When the pole is rotated, the string becomes horizontal and the tension and speed of the bead need to be calculated. Using a free body diagram, the problem can be solved by finding the length of the horizontal side of a right triangle with sides of 40 cm and 80 cm. The tension can then be determined as the force in the horizontal direction, and the speed can be easily calculated.
  • #1
Joelseph
2
0

Homework Statement


A 100 g bead is free to slide along an 80 cm long piece of string ABC. The
ends of the string are attached to a vertical pole at A and C, which are 40
cm apart. When the pole is rotated about its axis, AB becomes horizontal.
(a) Find the tension in the string. (b) Find the speed of the bead at B.


Homework Equations


F=ma
a=v^2/r



The Attempt at a Solution


I have drawn a free body diagram, and it is a right angle triangle with the vertical side being 40cm, and the other 2 sides being 80 in TOTAL but I'm not sure how to figure out the angles or sides with that little information.

Please assist. Once I have that information, the tension of the string is the force in the horizontal direction, and the speed will be easy enough to find as well.

Thanks
 
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  • #2
If x is the length of the horizontal side then X^2 + (40)^2 = (80 - x )^2
Solve for x.
 
  • #3
Gotcha, thanks for the help that was perfect.
The classic 3-4-5 triangle!
 

FAQ: How Do You Calculate Tension and Speed in Rotating Bead Physics Problems?

What is meant by centripetal circular motion?

Centripetal circular motion refers to the motion of an object traveling in a circular path at a constant speed. The direction of the object's velocity is constantly changing, but the magnitude of its velocity (speed) remains constant. This type of motion is possible because of the centripetal force acting on the object, which is always directed towards the center of the circle.

What is the difference between centripetal and centrifugal force?

Centripetal force is the inward force that causes an object to move in a circular path. It is always directed towards the center of the circle and is necessary to maintain the object's motion. On the other hand, centrifugal force is a fictitious force that appears to push an object away from the center of the circle. In reality, it is just the tendency of an object to continue moving in a straight line, and it is not an actual force.

How is centripetal force calculated?

The formula for calculating centripetal force is F = mv²/r, where F is the centripetal force, m is the mass of the object, v is its velocity, and r is the radius of the circle. This formula is based on Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.

What is the relationship between centripetal force and speed?

In circular motion, the centripetal force required to keep an object moving in a circle is directly proportional to the speed of the object. This means that as the speed increases, the centripetal force required also increases. This relationship can be seen in the formula for centripetal force, where the force is directly proportional to the square of the velocity.

What is the role of centripetal force in everyday life?

Centripetal force plays a significant role in many everyday activities. For example, the forces acting on a car as it goes around a curve are centripetal forces, which allow the car to maintain its circular motion. Similarly, the forces that keep a satellite in orbit around the Earth are also centripetal forces. Other examples include amusement park rides, such as roller coasters and carousels, and the motion of spinning objects, like a spinning top or a spinning ball on a string.

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