The Physics Behind Parking :: physics science cars vehicles

Background: After a long day of cruising through town with your buddy, the two of you have grown quite an appetite. You spot a McDonalds at the top of a very steep hill. Unfornately a local biker gang must of had the same idea. Encredibly, the only available parking spot is on the street, uphill of nearly 15 Harleys. There are no other restaurants for 100 miles in all directions. Famished, your friend skillfully manuvers his car to the side of the road. The breaks shudder as the car comes to a stop on the hill. He holds the brake, puts it into first, and shuts off the car. Problem: Biker's don't take kindly to people messing with their bikes. Your friend is about to let off of the brake. Being the physics major you are, you have to decide whether it's safe to park or safer to go hungry. Your friends car is pretty old, and the e-brake hasn't worked for years. The car will be held in place solely by the moter. There are two mean looking bikers smoking outside entrance. They are watching you so there probably wouldn't be time to make a run for it. Known What You Know: Your buddy's car is classic, and I'm sure he would want to make more than an educated guess. I've done a little investigating to help you out a bit. I took a torque wrench to the motor, and resists it resists aproximately 46 ft*lbs of torque at the crankshaft. After the compression bleeds down this number is reduced to 38 ft*lbs. The cars rear differential has a 3.73 to 1 gear ratio and a manual transmission with a 3.35 to 1 ratio in first gear. The tires are 28 inches in diameter and the gross weight of the car is approximately 2100 lbs. The hill is often travelled by truckers, and on the way up you noticed a sign that said the hill was at a 26 degree angle with the horizontal. Summary: When the car is at rest this means it is in a system of static equilibrium. Gravity is pushing forward on the car, and the tires are pushing back on the car via the reaction force of friction in the motor. The steeper the hill, the greater the force of gravity acting on the car, the greater the reaction force in the motor must have. As stated before, the maximum torque that can be applied to the motor before it rotates is 38 ft*lbs.