The document discusses the dynamics of a simple pendulum with a mass of 0.1 kg and a length of 0.4 m, providing calculations for its energy and speeds at various points. It calculates the tension in the string at position B, the speed at point C, and the speed at point B, assuming conservation of energy throughout the pendulum's motion. Key results include a tension of approximately 0.85 N, a speed of 2.8 m/s at point C, and a speed of 2.6 m/s at point B.

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