 # A small rock with mass 0.12 kg is fastened to a massless string with length 0.80 m to form a pendulum. The pendulum is swinging so as to make a maximu snowlovelydayM 2021-02-04 Answered
A small rock with mass 0.12 kg is fastened to a massless string with length 0.80 m to form a pendulum. The pendulum is swinging so as to make a maximum angle of 45 with the vertical. Air Resistance is negligible.
a) What is the speed of the rock when the string passesthrough the vertical position?
b) What is the tension in the string when it makes an angle of 45 with the vertical?
c) What is the tension in the string as it passes through the vertical?
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a) $mgl\left(1-\mathrm{cos}\left(\theta \right)\right)=\frac{1}{2}m{v}^{2}$
solve for v
$v=\sqrt{2gl\left(1-\mathrm{cos}\left(\theta \right)\right)}$
$v=\sqrt{2\left(9.8\right)\left(0.8\right)\left(1-\mathrm{cos}\left(45\right)\right)}$

b) $T-mg\mathrm{cos}\left(\theta \right)=0$
$T=mg\mathrm{cos}\left(\theta \right)$

c) $T-mg=m\frac{{v}^{2}}{r}$