Question

A pendulum of length 76 cm and mass 2.4 kg swings with a mechanical energy of 0.028 J. What is the amplitude?

Answer 1

0.042m or 4.2cm

Step-by-step 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 =
`(1)/(2 )mw^(2)A^(2)`

where
`w=\sqrt{(g)/(L) }` and g is acceleration due to gravity = 9.8m/s

inputting the value of
`w` into E =
`(1)/(2)m[\sqrt{(g)/(L) }]^(2)A^(2)`

0.028j =
`(1)/(2)* 2.4* [\sqrt{(9.8)/(0.74) }]^(2)A^(2)`

making A subject of formula and calculating it value

`A=\sqrt{(0.028)/(15.9)}=0.042m=4.2cm`