Question

1. A ball of mass m = 1.0 kg is suspended from the ceiling by a massless string of length L = 1.5 m. It is pulled to one side and started moving in a horizontal circular path, where it makes one revolution every 2 seconds. a) What is the angle that it makes with the vertical? b) What is the tension in the string? (30 points)

Answer 1

Tcose / Fc em Tsir mg

Consider the figure

-----------(1)

sino =

-----------------------

Given that the ball makes 1 revolution every 2s.

So speed of the ball, ----------(2)

21

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Consider all horizontal forces

F = 0

T sind - Fe=0

T sint = F.

m2,2 Tsint =

Put (1) in the above equation

$T*\frac{r}{L}=\frac{mv^{2}}{r}$

Т%

Put (2) in the above equation

* T* = m(**)

=m *

$T*\frac{1}{L}=m*\frac{4\pi^{2} }{t^{2}}$

$T*\frac{1}{1.5m}=1kg*\frac{4\pi^{2} }{(2s)^{2}}$

$T*\frac{1}{1.5}=1*\frac{4\pi^{2} }{2^{2}}$

$T=\frac{4\pi^{2} }{2^{2}}*1.5$

(b)ANSWER: ${\color{Red} T=14.8N}$

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Consider all vertical forces

$\sum F_{y}=0$

$Tcos\theta -mg=0$

$Tcos\theta =mg$

mg cost = I

$\theta =cos^{-1}(\frac{mg}{T})$

$\theta =cos^{-1}(\frac{1kg*9.81m/s^{2}}{14.8N})$

$\theta =cos^{-1}(\frac{1*9.81}{14.8})$

(a)ANSWER: ${\color{Red} \theta =48.48^{\circ}}$

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