Answer to Question #207096 in Mechanics | Relativity for Tiisetso

Question

A 2.00 kg mass hangs from the ceiling. The length of the string that attaches the mass at its center of gravity to the ceiling is 85 cm. The mass is pulled away from this vertical position so that it makes an angle of 20˚ with respect to the vertical. The mass is released from this position in a frictionless environment and allowed to oscillate. Calculate the maximum velocity of the mass. (6)

Answer 1

Solution.

$m=2.00kg;$

$l=0.85m;$

$\alpha=20^o;$

$\dfrac{a}{2}=lsin\dfrac{\alpha}{2};$

$a=2lsin\dfrac{ \alpha}{2};$

$a=2\sdot0.85\sdot0.1736=0.295m;$

$h=asin10^o=0.295\sdot0.1736=0.051m;$

$mgh=\dfrac{mv^2}{2};$

$gh=\dfrac{v^2}{2}\implies v=\sqrt{2gh};$

$v=\sqrt{2\sdot10\sdot0.051}=1m/s;$

Answer: $v=1m/s.$