Forces car of mass question

[adam112]

i have this question for an engineering science assignment, and can't remember how to work it out, any help would be greatly appreciated.

Question:
A car of mass 1500kg has a max speed of 144km/h up an incline of 1 in 49 against a frictional resistance of 500N. Calculate the power of the engine.

 

[denverdoc]

Neglecting the usual frictional losses in the engine and drivetrain, air resistance, etc, which reduce auto efficiency to about 25%, it would seem at a steady state where acceleration=0, whatever force being generated is just equal to the opposing gravitational force and frictional force. I would think then that you need to look at the displacement, both vertical and against friction to compute the work done by the engine. Hope that's a help as one is supposed to show work prior to any major assistance being given.

 

[m2003]

I would recommend approaching this question by first understanding the concept of power and how it relates to the given scenario. Power is the rate at which work is done or energy is transferred. In this case, the car's engine is doing work by overcoming the resistance of friction to move the car up the incline.

To calculate the power of the engine, we can use the formula P = F x v, where P is power, F is force, and v is velocity. In this scenario, the force we are interested in is the net force, which is the force produced by the engine minus the force of friction. We can calculate the net force by using the formula Fnet = ma, where m is the mass of the car and a is the acceleration.

To find the acceleration, we can use the formula a = (v^2 - u^2)/2s, where v is the final velocity, u is the initial velocity (in this case, 0), and s is the distance traveled up the incline. Plugging in the given values, we get a = (40^2 - 0^2)/2(49) = 0.816 m/s^2.

Now, we can calculate the net force by using Fnet = ma = (1500kg)(0.816 m/s^2) = 1224 N. To find the engine's power, we can plug in this value for force and the given velocity of 40 m/s into the formula P = F x v. This gives us P = (1224 N)(40 m/s) = 48,960 watts or 48.96 kW.

In conclusion, the power of the engine in this scenario is 48.96 kW. It is important to understand and apply the relevant formulas and concepts to solve engineering science problems like this. I hope this explanation helps and good luck with your assignment!