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7. Following graph is the chain gear system of a bicycle. The crank `Rc = 20.0\ cm`, `R_1 = 10.0\ cm`, `R_2 = 5.00\ cm` and `R_w = 30.0 cm`. If `F_(i n) = 500\ N`
a) Find tension `T` on the chain?
b) If the total mass of biker and bicycle is `100\ kg`. What is the the acceleration of the bicycle?
7. Following graph is the chain gear system of a bicycle. The crank Rc = 20.0\ cm, R_1 = 10.0\ cm, R_2 = 5.00\ cm and R_w = 30.0 cm. If F_(i n) = 500\ N
a) Find tension T on the chain?
b) If the total mass of biker and bicycle is 100\ kg. What is the the acceleration of the bicycle?  Wheel and axle: `τ_(i n) = τ_(out)`
a)
`T = 1000\ N`
b)
`a = 1.67 m//s^2`
Given:
`R_c = 20.0\ cm`
`R_1 = 10.0\ cm`
`R_2 = 5.00\ cm`
`R_w = 30.0 cm`
`F_(i n) = 500\ N`
Wheel and axle: `τ_(i n) = τ_(out)`
Solution:
a)
`τ_(i n) = τ_(out)`
`=>`
`F_(i n) R_c = T R_1`
`T = F_(i n) R_c /R_1`
`T = ( 500\ N) (20.0\ cm) /(10.0\ cm)`
`T = 1000\ N`
b)
Given: `M = 100 kg`
`τ_(i n) = τ_(out)`
`=>`
`TR_2 = F_(out)R_w`
`F_(out) = T R_2/R_w`
`F_(out) =(1000\ N)(5.00\ cm)/(30.0\ cm)`
`F_(out) = 167\ N`
`F_(out) = Ma`
`a = F_(out)/M`
`a = (167\ N) / (100 kg)`
`a = 1.67 m//s^2` |