Minimum work needed to push object up an incline?

What is the minimum work in kj needed to push a 1015.4-kg car 871 m up along a 9.0潞 incline? Ignore friction.





Please help!!Minimum work needed to push object up an incline?
the difference between the initial energy state, and the final energy state, is simply the height. in other words, the car would have gained gravitational potential energy.





if you draw a 9 degree right triangle, the opposite would be the height, and the hypotenuse would be 871 m (the length of the ramp). so,





sin 9 deg = h/871





=%26gt; h = 871 sin 9





we know m (mass of car) and (acceleration due to gravity)





simply use the above values in mgh





mgh = (871 sin 9) x 1015.4 x 9.81


= 1.36 x 10^3 KJMinimum work needed to push object up an incline?
Let work energy WE = mgh; where m = 1015.4 kg, g = 9.81, h = L sin(theta), and L = 871 m and theta = 9 deg incline. You can do the work





Given you are asking for help on this very rudimentary problem, I think you need a physics lesson more than answer this problem.





The physics is this, WE = Fs is the so-called work function. F is a net force acting along the direction an object m is moved a distance s. In your problem, the only force is the force of gravity, F = W = mg which we call weight. This is true because you discounted friction.





As gravity is always acting inward towards the center of mass M, in this case Earth's mass, it is always acting vertically wrt the ground. So as you push the object up the incline, the only force you are working against is the vertical force of gravity W. And because it is vertical, we need not consider any horizontal components in the work function. That is, we are just concerned with how high h = L sin(theta) the object is raised against the force of gravity.





In other words, in the work function WE = Fs, F = W = mg, the weight of the object, and s = h = L sin(theta) the height to which the object is raised above the starting point for pushing the object up hill. Therefore WE = Fs = mgh. And that's the physics you should learn. With that firmly entrenched, you can work any number of these kinds of problem.
First you will need to find the force required to push the car. You can do this using trig. (let the force of gravity parallel to the incline equal Fgx)





Fg = mg


Fg = (1015.4) (-9.8)


Fg = -9950.92 N





Fgx = sin(9) (-9950.92)


Fgx = -1556.67 N





Fa = -Fgx


Fa = 1556.67 N





To find work applied you multiply the force applied by the distance the car is pushed.





Wa = Fa x d


Wa = (1556.67) (871)


Wa = 1355856.82 J





Wa = 1355.86 KJ is your answer





Note: The is an alternative method to solving this problem. Since you are told to neglect friction you could simply find the hight of the ramp and multiply that by the weight of the object. If there is no friction, the work done to raise the object straight up would be the same as if you pushed the object up the incline.