Hi guys can some one help me with this question.
So a 2.5kg mass is rotated in a conical pendulum where the length of the string is 0.68 metres and thr angle between the string and the vertical is 35 degrees.
Find
a. The tension in the string
b. The speed of the mass
If the pendulum is now spun faster so that it's period is now 1.2 seconds find
A. The tension in the string
b. The angel the string makes with the vertical
q1:
a. net force vertically on the mass is 0 newtons, therefore downward force due to weight=upward force due to tension.
T cos(35)=mg=2.5 * 10=25 therefore T=30.5 N
b. net force horizontally is equal to T sin(35)=17.5 N.
a=F/m=7 ms^-2
r=0.68 sin(35)=0.39 m
v^2=ar=2.73 --> v=1.65 ms^-1
q2: remember mass is still 2.5 kg and length of string is still 0.68 m
a. r=0.68 sin(θ), v=2πr/T=3.56 sin(θ)
a=v^2/r=18.6 sin(θ)
F=ma=46.6 sin(θ)
horizontal component of tension force=T sin(θ) --> T=46.6 N
b. vertical component of tension force=T cos(θ)=mg
46.6 cos(θ)=25
cos(θ)=0.54
θ=57.6 degrees
Hope this helped!
edit:
How do I express direction in terms of degrees. eg. 53.1 degrees counterclockwise from the ground (is there a more "scientific" way to express this?)
53.1 degrees from the horizontal is probably best. I definitely wouldn't use bearings.