Question

An 87 cm long pendulum with a 0.60 kg bob is released from rest at an initial angle of ?0 with the vertical. At the bottom of the swing?, the speed of the bob is 2.8 m/s.

9. -/10 points Tipler6 7.P.052. My Notes An 87 cm long pendulum with a 0.60 kg bob is released from rest at an initial angle of 8o with the vertical. At the bottom of the swing, the speed of the bob is 2.8 m/s. (a) What is θ。? ) What angle does the pendulum make with the vertical when the speed of the bob is 1.4 m/s? Is this angle equal to (%)Po? O yes no Explain why or why not. This answer has not been graded yet. eBookPicture It Submit Answer Save Progress Submit AnswerSave Pro

Answer 1

a) Energy is conserved.We have,
0.5mv^2+mgh=const.
in this problem 0.5 mv^2+mg*l(1-cosθ)=const.
0.5 mv^2=mg*l*(1-cosθ_0)
0.5v^2=gl(1-cosθ_0)
θ_0= 57.3 degree.

b) We have
0.5mv'^2+mgl(1-cosθ')=mgl(1-cos57.3).
0.5 v'^2+glcos57.3=glcosθ'
so θ'=49.07 degree

No θ' is not half of θ_0