Question

How to resolve power of an object on inclined planes?

A car of mass 2000 kg travels up a slope of 30.0° at a uniform speed of 15.0 m s-1.If the frictional resistance is 10% of the weight of the car, at what power is the engine working?

Answer 1

`P= 1.7658 xx10^5W`

Explanation:

`Power = "Workdone"/"time" = "Force x distance"/"time"= "Force x velocity"`

Since the speed "v" is given is given, apply

`P= Fv`

From Newton's second law

`F = mgsintheta+0.1mg = mg(0.1+sin30^@)=0.6 mg`

`rArr P= Fv = 0.6mgv=0.6*2000kg*9.81m/s^2*15.0m/s`
`P= 1.7658 xx10^5W=176.6 kW`

Force explanation:
Note that car is traveling uphill at constant speed, hence the net force must be zero. There are 3 forces acting on the car, the force (F) of the engine pushing the car uphill, the gravitational pull modified by the slope (`mgsintheta`) and the friction (0.1mg)

`F_"net"=0`

`F_"net" = F_"Engine" - "gravitation pull" - "frictional force" = 0`

`F_"Engine"= mgsintheta+0.1mg = mg(sintheta+0.1)= 0.6 mg`

Label `F = F_"Engine" = 0.6 mg`