Solving Vertical Circular Motion Homework Problems

[songoku]

Homework Statement

1. A ball is tied to a string then moved so that its trajectory is vertical circle. If the mass of the ball is 500 g, the speed is 2 m/s, and the length of string is 50 cm, find the tension when it is at the top of the trajectory

2. A mass m is tied to a string and moved so that its trajectory is vertical circle. The maximum and minimum value of the tension are 90 N and 10 N respectively. Determine the mass and linear speed of the mass

Homework Equations

F = mv²/r
W = mg

The Attempt at a Solution

1. T = mv²/r - mg = 4 - 5 = -1 N ?
It is possible that at the top of its motion, the tension becomes loose and yet it still moves in circle? If not, where is my mistake?

2. maximum when it is at bottom and minimum when it is at top
at bottom: 90 = mg + mv²/r
at top: 10 = mv²/r - mg

By elimination, I got m = 4 kg but I can't find v. Any suggestions?

Thanks

 

[kuruman]

These are not well-posed questions. Your analysis of 1 is correct. If the tension is negative, this means that the string is loose and the path of the mass is as in free fall, a parabolic trajectory and no longer a circle. Question 2 does not specify the length of the string and does not say that the mass is moving at constant speed. If you assume that the string has length 50 cm as in the previous problem and that the mass moves at constant speed, then you should be able to answer the question because you have the correct equations.

 

[songoku]

Sorry for replying now

Is it better to answer T = 0 N or T = -1 N? (I think it's impossible tension has negative value)

Thanks

 

[kuruman]

It is better to answer T = 0. You can't push on something with a rope.

 

[songoku]

Ok. Thanks kuruman