Circular Motion - Finding Tension

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SUMMARY

The discussion focuses on calculating the tension in a string when a ball of mass 0.300 kg is revolved in a vertical circle with a radius of 65.0 cm at a speed of 4.00 m/s. The tension is determined using the net force equation Fnet=ma and centripetal acceleration derived from the formula v^2/r. At the top of the circle, the tension is calculated to be 4.44 N, while the method for calculating the tension at the bottom of the path is also outlined, emphasizing the importance of free body diagrams in visualizing forces.

PREREQUISITES
  • Understanding of centripetal acceleration and its calculation using v^2/r
  • Familiarity with Newton's second law, specifically Fnet=ma
  • Ability to draw and interpret free body diagrams
  • Basic knowledge of gravitational force calculations (mg)
NEXT STEPS
  • Calculate the tension in the string at the bottom of the circular path using the same principles
  • Explore the effects of varying mass and speed on tension in circular motion
  • Study the role of gravitational force in vertical circular motion scenarios
  • Learn about the dynamics of non-uniform circular motion and its impact on tension
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators preparing quiz materials on tension and forces in circular dynamics.

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Homework Statement


A ball on the end of a string is cleverly revolved at a uniform rate in a vertical circle of radius 65.0 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.
(b) Calculate the tension in the string when the ball is at the bottom of its path.

Homework Equations


Fnet=ma
v^2/r=a


The Attempt at a Solution


This is for my quiz review packet which is unfortunately due tomorrow, and I'm confused about how to solve this problem.
I'm thinking that since this problem involves tension I'm going to need the equation Fnet=ma.
To find A first I take the velocity 4m/s and put it to the power of 2, so its (16m/s)/radius= centripetal acceleration)
In this case 16/.65=a so 24.62m/s is the acceleration
Fnet at the top of the circle is mg+t (.300)(9.81)+t
2.94300+X=.300*24.62
2.94300+x=7.38600
4.44300=x

If this is right I know how to do the second part.
 
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To start, draw a free body diagram of both situations to see all the forces acting on the objects and how they're acting. Then come up with a Fnet statement, by looking at all the forces.
 
That is right.
 

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