The Physics of Moving a Car

 

Last night my sister packed up and tried to drive home, only to discover that she left a light on in her car, effectively killing the battery. One would expect the story to end here with an easy jumpstart and my sister on her way in under thirty minutes. However, there was one roadblock; the tree on my front lawn. My driveway is long and thin, slopes downhill, and consists of many loose stones. Because it is roughly the width of one car, one car cannot pass by another without going on the grass. My sister had conveniently parked in between two trees, making it impossible to pass her with my dad’s car in order to get their engines close enough to jumpstart her car. My dad decided that this left us with only one option: we must push the car up our driveway. 

Originally my brother and I had questioned this, wondering why we would not push the car further down the driveway. Surely the force of gravity would help us in pushing the car, effectively lessening the work we would have to do. This is because if we are pushing the car down the hill, the force of gravity in the x direction will be pointing in the same direction and will also contribute work in the same direction of our force. Pushing the car up the hill would be applying a force against both friction and the force of gravity, requiring more work (or a larger applied force) on our part to combat this and initiate movement. 

However, the important component we did not consider is that distance plays a role in the work done on a system. All other elements the same including friction, applied force, and force due to gravity, there will be some instance in which a larger distance required of the downhill push will make it less advantageous with a larger net work required. Because of the location of my house right after the trees, we would have had to push the car 20 meters into my backyard as opposed to 5 yards up my driveway.  

Setting net work equal to 0 J because this is what the work would be just before we push the car into motion, we can solve for the applied force necessary to move the car in each instance. Given that the downhill journey would require work for about 20 meters and the uphill journey would require work for about 5 meters, the downhill journey requires an applied force of 19000 N in comparison to the uphill applied force of about 3000 N. 

https://www.engineersedge.com/coeffients_of_friction.htm

https://hondanews.com/en-US/honda-automobiles/releases/release-3f07e0920c854addbd2284bad4720cee-2018-honda-fit-specifications-and-features