What is the minimum work needed to push a 800 kg car 860 m up along a 9.0 degree incline? Ignore friction. Then assume the effective coefficient of friction retarding the car is 0.22. I have no idea where to start this problem

no friction? work= mgh= mg*860sin9

friction? friction= mg*mu*cos9* 860
min work= mgh+mg*mu*cos9*860

You start the problem by applying basic, fundamental relationships.

I am not understanding how to do the second part...assume the effective coefficient of friction retarding the car is 0.22. I got the first part and the answer is 1.1*10^6, how do I figure out the second part?

see the last two lines of my response. Solve for min work.

To solve this problem, you can break it down into two parts: the work done to push the car up the incline and the work done to overcome friction.

1. Work to push the car up the incline:
The work done to push an object up an incline is equal to the force applied multiplied by the distance over which the force is applied.

First, let's calculate the force required to push the car up the incline. The force can be found using the formula:

Force = Mass x gravity x sin(theta)

Where:
Mass = 800 kg (given)
Gravity = 9.8 m/s^2 (acceleration due to gravity)
theta = 9.0 degrees (given)

So, Force = 800 kg x 9.8 m/s^2 x sin(9.0 degrees).

Next, calculate the distance over which the force is applied. In this case, it is given as 860 m.

The work done to push the car up the incline is given by:

Work = Force x Distance

Substituting the values we found:

Work = (800 kg x 9.8 m/s^2 x sin(9.0 degrees)) x 860 m.

2. Work done to overcome friction:
The force of friction can be found using the formula:

Force of friction = coefficient of friction x normal force

The normal force can be found using the formula:

Normal force = Mass x gravity x cos(theta)

Where:
Mass = 800 kg (given)
Gravity = 9.8 m/s^2 (acceleration due to gravity)
theta = 9.0 degrees (given)

So, Normal Force = 800 kg x 9.8 m/s^2 x cos(9.0 degrees).

Next, calculate the force of friction using the given coefficient of friction of 0.22.

Force of friction = 0.22 x (800 kg x 9.8 m/s^2 x cos(9.0 degrees)).

Finally, calculate the work done to overcome friction using the formula:

Work = Force of friction x Distance

Substituting the values we found:

Work = (0.22 x (800 kg x 9.8 m/s^2 x cos(9.0 degrees))) x 860 m.

The total work done to push the car up the incline while also overcoming friction is the sum of the work done to push the car up the incline and the work done to overcome friction:

Total work = Work to push up the incline + Work to overcome friction.

Calculate the two parts separately and add them to get the total work required.