Question

A 1210 kg car is driving on 60 km/h on an inclined plane. The car is located on the top of the plane. The plane is 655 m long and the angle is 4.50 degrees.

a) What will the speed of the car be if there is no friction ?

b) Now the car is on 85 km/h at the bottom of the inclined plane. How much friction force works on the car its way down ?

c) If the same friction force works on the car as when it drow up the plane, what does the mechanical power need to be so the car can drive on 85 km/h ?

d) Lets assume thet the same friction force works on the car that drives in a normal driving. How much gas will the car spend on a hundred ef the heat of reaction of the gas is 38 MJ/liters and the efficiency is 21 %

Help please.

Answer 1

Let's begin with the forces on the car, without friction:

Weight ( w), Normal force. Drawing the body free diagram we can obtain these movement equations using Second Law of Newton:

                    

Look that there's equilibrium on y axis, but not on x axis. With x equation, you can obtain acceleration so you can use kinematics to obtain velocity at the bottom covering a distance of 655 m with an initial velocity of 60 km/h:

   REmember unit convertions from km to meters, and hour to seconds.

This part can be easily obtain by another method, using conservation of energy but I don't know if you have maybe you do so:

Energy at the top: Potential and kinetic energy

Energy at the bottom: kinetic energy.

    you can resolve for final velocity and should obtain the same result from above. h, height can be obtain by trigonometric function, sine.

For part b. take into account that the velocity with friction will be less than without it, so friction must be doing work on the car to slow it down. We can add a force for x axis and reverse the procedure or use conservation energy knowing that there will be a lost energy by friction:

     and use the same kinematic equation but first obtain acceleration from the kinematic equation and then use it for the force equation to obtain f (friction).

or by energy: Same energies at the top and at the bottom but remembering that there's an energy that it will be spent by friction:

  

Remember again unit conversion. With the negative sign it says that work done by friction is negative because it makes mechanical energy to be lost a fraction of it. You can say also that     or Which are the same.

part c) Mechanical power refers to force multiply it by velocity. You have now force of friction from point b) now multiply it for 85 km/h, changing units to m/s.

d) I don