mechanics help! (1 Viewer)

[fahadmumtaz88]

I tried this question but the answer in the back seems to be different, can someone help me out? thanks

The questions are:

1) If a conical pendulum is 1.4m long and the semivertex angle of the cone is 30 degrees find the period of rotation adn the tension in the string when the mass of the particle is 10 kg.



2) An inextensible string of length 2m is fixed at one end and carries at its other end B a particle of mass 6 kg which is rotating in a horizontal circle whose centre is 1m vertically below A. Find the tension in the string and the angular velocity of the particle.

 

[KFunk]

The questions are:

1) If a conical pendulum is 1.4m long and the semivertex angle of the cone is 30 degrees find the period of rotation adn the tension in the string when the mass of the particle is 10 kg.

Let the tension in the string be T.

∑ vertical forces = 0 ,

i.e. Tcos30° = mg ,
T = mg/cos30° = 200/√3 N

*note: this is the same as 20 √3/3 kg wt ... fitz notation is retarded

∑ horizontal = mw²r

Tsin30° = mw²r
w = √[Tsin30°/mr] where r = 0.7m

then T = 2π/w which is 2. something seconds

 

[KFunk]

2) An inextensible string of length 2m is fixed at one end and carries at its other end B a particle of mass 6 kg which is rotating in a horizontal circle whose centre is 1m vertically below A. Find the tension in the string and the angular velocity of the particle.

Let the tension in the string be T and note that the lengths given create that basic triangle with angles 30, 60 and 90°

∑ vertical = 0 so Tcos60° = mg
T = 2mg (1)

∑ horizontal = mrw²

Tsin60° = mrw²

mg√3 = mrw² from (1) ∴ w = √(√3g/r)

[put the values in to get your numerical answer. I'm not sure what values of g you're using]