A car of mass 1000 kg moves up at `40 km *h^(-1)` along an inclined plane of slope `1/(50)` . Coefficient of rolling friction between the road and the wheels of the car is 0.3. Find the power of the car engine.

Explanation

Angle of inclination `=theta` [Fig.1.27].

`therefore` Slope
`=tan theta =1/(50)~~sin theta`
`[because theta` is small]
Resultant downward force on the car along the incline
`=mg sin theta +f`
`=mg sin theta +muR`
`=mg sin theta +mu mg cos theta =mg (sin theta +mu cos theta)`
=`1000xx 9.8 (1/(50)+0.3xx1)` [as `theta` is very small , `cos theta cosn1`]
`= 9800xx0.32=3136N`
Velocity of the car =`40 km*h^(-1) =11.11m*s^(-1)`
`therefore` Power of the car =`3136xx11.11 N *m*s^(-1) =34840 .96 W =34.84 kW.`