88.1 Work done by variable force Solution: From the force diagram x component: F-Tsin=0 y component: T cos o-mg=0 Eliminate T we find F=mg tang H=∫F·dF=∫rd mg tanddx=. mg tandd( Lsin g) o mgL sindo=mgL (1-cos gm) 88.1 Work done by variable force Wn=「TdF=0 Wn=[.-mgj·dF L-Lcos中m mgd mg L-Lcos ou) w=W+W+W=0I 88 Solution: From the force diagram F = mg tanφ Eliminate T, we find sin d (1 - cos ) tan d tan d( sin ) d d m 0 φ φ φ φ φ φ φ mgL mgL mg x mg L W F r F x m f i f i f i f i F = = = = = ⋅ = ∫ ∫ ∫ ∫ ∫ r r x component: y component: cos 0 sin 0 − = − = T mg F T φ φ §8.1 Work done by variable force ( cos ) d d ˆ d 0 cos 0 m L L f i g T mg L L mg y W mgj r W T r m φ φ = − − = − = − ⋅ = ⋅ = ∫ ∫ ∫ − r r r = + + = 0 W WF WT Wg §8.1 Work done by variable force r r d