1. 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

2. a  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.

3. 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 a Find: the initial acceleration a of the vehicle as no slipping on the wheels.

4. 1.Design coordinate  coordinate ： 0 (I,J,K) Ω=0

5. 2.kinematics  R G =XI

6. 3.work-Energy Equation  δ∫2TdR G = δ[(1/2)m(R G )^2+2(1/2)I A (W A )^2+(1/2)I C (W C )^2-mgR G cosθ a  -2T δX=ma G δx+2I A W A δW A +I C W C δW C -mgsinθ δx a =ma G δx+2I A R G /R A δR G /R A +I C R G /R C δR G /R C -mgsinθ δx a =ma G δx+2I A (1/R A )^2a G δx+I C (1/R C )^2a G δx-mgsinθ δx ------1 IA=140*(0.15)^2=3.15 ------2 IC=40*(0.1)^2=0.4 ------3 a 整理 1 ： a G = (mgsinθ-2T)/m+ 2I A (1/R A )^2+ I C (1/R C )^2 a 帶入 2,3 ： a G =0.341 m/s^2