Answer:
0.042m or 4.2cm
Explanation:
Given
length of pendulum (L) = 76cm = 0.76 m
mass of object (m) = 2.4kg
total mechanical energy (E) = 0.028 joules
amplitude(A) = ?
formula for total mechanical energy of a pendulum is
E = [tex]\frac{1}{2 }mw^{2}A^{2}[/tex]
where [tex]w=\sqrt{\frac{g}{L} }[/tex] and g is acceleration due to gravity = 9.8m/s
inputting the value of [tex]w[/tex] into E = [tex]\frac{1}{2}m[\sqrt{\frac{g}{L} }]^{2}A^{2}[/tex]
0.028j = [tex]\frac{1}{2}\times 2.4\times [\sqrt{\frac{9.8}{0.74} }]^{2}A^{2}[/tex]
making A subject of formula and calculating it value
[tex]A=\sqrt{\frac{0.028}{15.9}}=0.042m=4.2cm[/tex]
