- #1
SnowboardNerd
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Homework Statement
A mass m = 16.0 kg is attached to the lower end of a massless string of length L = 63.0 cm. The upper end of the string is held fixed. Suppose that the mass moves in a circle at constant speed, and that the string makes an angle theta = 17o with the vertical, as shown in the figure. How long does it take the mass to make one complete revolution?
Homework Equations
T = 2 pi r / v
F = m a
Ac = v^2 / r
The Attempt at a Solution
m = 16
L = 0.62 m
θ = 17
Drew a FBD...
It shows mg acting down upon the object, and T diagonally up.
Fx = m * ac
T sin theta = m ac
T sin theta = m * v^2/r
T sin theta = m * v^2/ L sin theta
Fy = m * ac
T cos theta - mg = 0
T cos theta = mg
T = mg /cos theta
Use the above and sub it in..
(mg/cos theta) sin theta = m (v^2) / L sin theta
√ ((( L (sin(theta))^2) g sin(theta))) / cos theta ) = V
V = (sqrt( (.63 (sin^2(17)) (9.8) sin(17) )/ cos(17)))
Use formula... T = 2pi r / v
(2pi(0.63*sin(17)))/(sqrt( (.63 (sin^2(17)) (9.8) sin(17) )/ cos(17)))
I get.. 2.88 seconds.
Where did I go wrong?? Thanks for your time!