Answer to Question #267551 in Classical Mechanics for wil

Question

The bob of the pendulum is 200 g. It is swinging at a height of 1 m. The length of the pendulum is 1 m. Find the values of GPE, KE, and total mechanical energy at a height of 1 m, 0.5 m and 0.25 m and at its lowest point.

Answer 1

$m = 200g = 0.2kg$

$g = 9.8\frac{m}{s^2}$

$E = GPE +KE$

$GPE = mgh$

$\text{for }h=1m$

$KE = 0$

$GPE = 0.2*9.8*1= 1.96J$

$E = 1.96J$

$\text{for }h=0.5m\newline E = 1.96J\newline GPE = 0.2*9.8*0.5=0.98J\newline KE = E-GPE = 1.96-0.98 =0.98J$

$\text{for }h=0.25m\newline E = 1.96J\newline GPE = 0.2*9.8*0.25=0.49J\newline KE = E-GPE = 1.96-0.49 =1.47J$

$\text{for }h=0m\newline E = 1.96J\newline GPE = 0\newline KE = E-GPE = 1.96J$