A city planner is working on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A pariticular small car, witha mass of 1100kg, can accelerate on a level road from rest to 21m/s (75km/h) in 14,0s using these data, calculate the maximum steepness of a hill.
2006-08-30 07:59:23 · 3 answers · asked by nice_ girl 1 in Science & Mathematics ➔ Physics
I won't do the problem for you, but I'll tell you HOW to do it:
The mass of the car, final speed of the car, and time it takes to reach that speed will give you the force which the engine can exert. This is assuming a "theoretical" case where the car accellerates at an even rate until it reaches the final velocity (real cars don't usually do that, but physics 101 cars always do!)
Now you need to figure out, using the acceleration value for gravity (32 f/s^2 -- I forget what it is in metric units but I'm sure you have that somewhere) and the vector formulas for forces acting on an object resting on an inclined plane, what angle of inclined plane produces that same level of force rearward (relative to the car) for an object of that car's mass.
The angle of the roadway must be less than or equal to that of the inclined plane -- if it were greater, the force of gravity acting rearward on the car would be greater than the force of the engine, and the car would decellerate until it came to a stop and then begin rolling backwards down the hill against the force of the motor.
2006-08-30 08:14:08 · answer #1 · answered by Mustela Frenata 5 · 0⤊ 0⤋
The mass of the car is irrelevant. The car can accelerate at 1.5 m/sec^2, which is roughly 0.15 gravity. The percent grade should not therefore exceed 15, i.e, at most 15 meters rise per hundred meters horizontal.
2006-08-30 15:07:53 · answer #2 · answered by Anonymous · 0⤊ 0⤋
You need to do your own homework!
2006-08-30 15:05:14 · answer #3 · answered by cass 2 · 0⤊ 1⤋