This question is the review for energy, and also combines the idea of simple pendulum which is good to be used to understand the motion of the pendulum as well as the equation for pendulum

1. Learningobjects – Simple Pendulum
In the belowfigure,thereisone pendulumswingsfrompointA,andat pointC it hasthe
greatestvelocity.The stringattachedtothe pendulumhasalengthof 0.4m and the pendulum
has a mass of 0.1kg. Whenthe pendulumswingstothe positionof B, θ=30o
. The total energyof
the systemdoesnotchange.
(1).Whenthe pendulumswingstopositionB,whatisthe magnitude of itsT?
(2).What is the speedof the pendulumwhenitcrossespointC?
(3).What is the speedof the pendulumwhenitisatpointB?
Figure 1.1
Answer:
(1).T=mg*cosθ
T=0.1kg*9.8N/kg*cos 30o
T=0.98N*0.87=0.85N
(2).At pointA,pendulumdoesnothave kineticenergy,andatpointC,it doesnot have
potential energy.The total energyof the systemdoesnotchange,som*g*h=
1
2
*m*v^2
9.8*0.4=0.5*v^2
V^2=7.84
V=2.8m/s
(3).The total energyof the systemdoesnotchange.To determine the speed,the heightmust
be determinedpriortothe speeditself. hB=0.4-0.35=0.05m

2. mgh=mghB+0.5mv^2
0.98*0.4=0.98*0.05+0.5*0.1*v^2
V=2.6m/s