動力學---第一組報告
P.485 Problem 6/164
教授：林穎裕
學生：杜長軒，陳莨融，鄭人豪
 The vehicle is used to transport supplies to and from the
bottom of the 25-percent grade . Each pair of wheels ,
one at A and the other at B , has a mass of 140 kg and a
radius of gyration of 150 mm . The drum C has mass of 40
kg and a radius of gyration of 100 mm . The total mass of
the vehicle is 520 kg . The vehicle is release from rest with
a restraining force T of 500 N in the control cable which
passes around the drum and the drum and is secured at
D . Determine the initial acceleration a of the vehicle .
The wheels roll without slipping .
Given: 1) a vehicle on 25-percent grade, having two pairs of
wheels at A and B, respectively, each mass of 140 kg
and a radius of gyration of 150 mm .
2) The drum C has mass of 40 kg and a radius of gyration of
100 mm. The total mass of the vehicle is 520 kg.
3) The vehicle released from rest with a restraining force T
of 500 N in the control cable
Find: the initial acceleration a of the vehicle as no slipping on
the wheels.
1.Design coordinate
 coordinate：0 (I,J,K) Ω=0
2.kinematics
 RG=XI
 RG=XI
3.work-Energy Equation
 δ∫2TdRG= δ[(1/2)m(RG)^2+2(1/2)IA(WA)^2+(1/2)IC(WC)^2-mgRGcosθ
 -2T δX=maG δx+2IAWA δWA+ICWC δWC-mgsinθ δx
=maG δx+2IARG/RAδRG/RA+ICRG/RC δRG/RC-mgsinθ δx
=maG δx+2IA(1/RA)^2aGδx+IC(1/RC)^2aGδx-mgsinθ δx ------1
IA=140*(0.15)^2=3.15
------2
IC=40*(0.1)^2=0.4
------3
整理 1 ：aG= (mgsinθ-2T)/m+ 2IA(1/RA)^2+ IC(1/RC)^2
帶入2,3 ： aG=0.341 m/s^2