Answer to Question #240214 in Physics for Sam

Question

. A car of mass 1000kg moving on a horizontal road with a steady velocity of 10m/s has a total frictional 

force on it of 400N. (a) Find the power due to the engine (b) the car now climb a hill at an angle of 80

to the horizontal. Assuming the frictional force remain constant at 400N, what engine power is now 

needed to keep the car moving at 10m/s

Answer 1

The power is force times speed. The force here is the force of friction because, according to Newton's first law, the body moves at constant velocity when the net force is zero (or when the thrust is equal to the force of friction).

$$P=fv=400·10=4000\text{ W}.$$

In this case, the engine also needs to overcome force of gravity along the slope, which is

$$F=mg\sin\theta.\\ P=(F+f)v=(mg\sin\theta+f)v,\\ P=(1000·9.8\sin8°+400)·10=17640\text{ W}.$$