Hi, can anyone help me with question 14 please? Am i right in thinking that the particle travels in a horizontal circle below AP but above BP? So that by resolving vertically you get TensionAcosX=mg +TensionBcosY?
Hi, can anyone help me with question 14 please? Am i right in thinking that the particle travels in a horizontal circle below AP but above BP? So that by resolving vertically you get TensionAcosX=mg +TensionBcosY?
Yes.
Depending on what the angles are that you're refering to.
Depending on what the angles are that you're refering to.
The angles I am referring to at the ones that the strings make with the vertical, if this is correct then how can I eliminate both tensions? I have found r using Pythagorus but still have too many unknowns
The angles I am referring to at the ones that the strings make with the vertical, if this is correct then how can I eliminate both tensions? I have found r using Pythagorus but still have too many unknowns
You're going to need the motion in a circle equation as well.
Note: You're not going to get a numerical answer - it's going to be a function of angular velocity.
So, put your two equations together and solve for T1 and T2. You should be able to put in values for the sines and cosines.
For T2, I got:
Spoiler
Ok I have found the two tensions and my T2 matches yours. how can i now prove w^2>5g/16a? If i sub my values for T1 and T2 back into the equation w^2 will just cancel out
Ok I have found the two tensions and my T2 matches yours. how can i now prove w^2>5g/16a? If i sub my values for T1 and T2 back into the equation w^2 will just cancel out
Consider the object you're modelling. What must be true of T2? (and T1 for that matter).
So i can't use T1 because the question asks for w^2 to be greater than or equal to the given value. I get the correct value for w but it's negative
You can't use T1 as it doesn't give any restriction on w. T1 > 0 even if w=0. A negative value of w is meaningless here, as we haven't given it a direction, clockwise or anticlockwise.
Think about it. The mass is moving in the shape of a conical pendulum. It's radius depends on how fast it is going. AP will always be taut, but BP will only be taut once the angular velocity exceeds a certain value, and the radius of the circular motion is large enough.
You can't use T1 as it doesn't give any restriction on w. T1 > 0 even if w=0. A negative value of w is meaningless here, as we haven't given it a direction, clockwise or anticlockwise.
Think about it. The mass is moving in the shape of a conical pendulum. It's radius depends on how fast it is going. AP will always be taut, but BP will only be taut once the angular velocity exceeds a certain value, and the radius of the circular motion is large enough.
Oh ok i understand be because a smaller angular speed will result in a smaller radius so the sting is slack but once the speed picks u and the radius increases the string can become taut. So I need to find this minimum value of the radius?
Oh ok i understand be because a smaller angular speed will result in a smaller radius so the sting is slack but once the speed picks u and the radius increases the string can become taut. So I need to find this minimum value of the radius?
You know the radius.
You need to know the value of omega that gives that radius, which is the same as the one that makes T2 >=0. Hence the calculations you've already done.
You need to know the value of omega that gives that radius, which is the same as the one that makes T2 >=0. Hence the calculations you've already done.
But subbing values for T1 and T2 into the calculations i have done eliminates omega, i don't know how I can make omega the subject apart from doing T2 greater than or equal to 0 which gives me a minus value for omega
But subbing values for T1 and T2 into the calculations i have done eliminates omega, i don't know how I can make omega the subject apart from doing T2 greater than or equal to 0 which gives me a minus value for omega
Why are you mentioning T1 again?
You just need T2 >=0. Post working if it's not coming out.