Why is it easier to move a car by pulling on a rope attached to a pole?

[Tearsandrille]

Homework Statement

You attach a strong rope or steel cable to a light pole and a car parked on a downhill incline. If you have a student lift, pull, or push perpendicularly on the rope in the center it will be easier to move the car than if you were to push it. Why? Prove this mathematically.

Homework Equations

The Attempt at a Solution

I know it has something to do with the tension, but I can't figure out exactly how it works.

 

[tiny-tim]

You attach a strong rope or steel cable to a light pole and a car parked on a downhill incline. If you have a student lift, pull, or push perpendicularly on the rope in the center it will be easier to move the car than if you were to push it. Why? Prove this mathematically.

Hi Tearsandrille!

(do you mean a lamp post? )

Hint: Suppose the rope has length L, and is at an angle θ to the direct line between the car and the lamp post … if you push it with force F in the middle, what is the force on the car?

 

[Tearsandrille]

I did mean lamp post. You'll have to excuse me there, my brain was friend trying to draw all the FBD and vectors.

So, wouldn't the force on the car be tan(theta) * Fapp.

My trig isn't so great, but how is that less than the force you would need to push the car? I believe in order to push the car it would be m*g*sin(theta).

 

[tiny-tim]

Hi Tearsandrille!

(just got up :zzz: …)

So, wouldn't the force on the car be tan(theta) * Fapp.

Nope.

Take components along the line of the F_app.