A bob of mass m is suspended from a fixed point with a massless string of length L (i.e., it is a pendulum). You are to investigate the motion in which the string moves in a cone with half-angle theta.
What tangential speed, v, must the bob have so that it moves in a horizontal circle with the string always making an angle theta from the vertical?
Express your answer in terms of some or all of the variables m, L, and theta, as well as the acceleration due to gravity g.
2006-10-04 17:03:29 · 5 answers · asked by agnobles 2 in Science & Mathematics ➔ Physics
It's not as hard as it looks if you think of things as components of vectors. Make sure you draw a picture and you will see the following relationships:
Tcos(theta) = mg
centripetal force = Tsin(theta)
R (radius of cone) = Lsin(theta)
since you know centripetal force = mv^2/R
1. Cf = mv^2/R = Tsin(theta)
2. Therefore, v^2 = R * Tsin(theta) / m
3. substituting from above, v^2 = L*g*sin^2(theta)/cos(theta)
2006-10-04 17:41:29 · answer #1 · answered by first l 1 · 13⤊ 2⤋
I can solve it. You have to figure out at what centripital acceleration it takes for the tension in the string to add up to the forces that will offset gravity and provide the necessary cent. acceleration.
2006-10-04 17:18:14 · answer #2 · answered by daedgewood 4 · 0⤊ 20⤋
Answer a :
v = Lsin(theta) / sqrt ( Lcos(theta)/ g)
Answer b :
2pi (Lsin(theta)) / sqrt (gLtan(theta)sin(theta))
2016-10-04 04:35:02 · answer #3 · answered by ? 1 · 8⤊ 1⤋
tick tock
or tether ball.
trying to draw that pic. in my head.
2006-10-04 17:10:03 · answer #4 · answered by Anonymous · 0⤊ 18⤋
not me
2006-10-04 17:05:08 · answer #5 · answered by JustMe 2 · 0⤊ 25⤋