Ask Your Teacher My Notes Question Part Points Submissions U

Ask Your Teacher My Notes Question Part Points Submissions Used It is said that Galileo discovered a basic principle of the pendulum—that the period is independent of the amplitude—by using his pulse to time the period of swinging lamps in the cathedral as they swayed in the breeze. Suppose that one oscillation of a swinging lamp takes 5.3 s.

(a) How long is the lamp chain?
m

(b) What maximum speed does the lamp have if its maximum angle from vertical is 3.1°?
m/s

Solution

a) T = 2pi sqrt(L/g)

5.3 = 2pi sqrt( L / 9.8 )

0.843 = sqrt(L/g)

L / g = 0.843^2

L = 6.96 m

b) height of lamp from lowest position.

h = L (1 - cos3.1)

h = 6.96 ( 1 - cos3.1) = 0.0102 m

using energy conservation,

m v^2 / 2 = mgh

v = sqrt(2gh)

v = sqrt(2 x 9.8 x 0.0102)

v = 0.447 m/s