In the Soapbox Derby, young participants build non-motorized cars with very low-
ID: 2273510 • Letter: I
Question
In the Soapbox Derby, young participants build non-motorized cars with very low-friction wheels. Cars race by rolling down a hill. The track at Akron's Derby Downs, where the national championship is held, begins with a 55ft-long section tilted 13?below horizontal.
What is the maximum possible acceleration of a car moving down this stretch of track?
If a car starts from rest and undergoes this acceleration for the full l, what is its final speed in m/s?
Express your answer to two significant figures and include the appropriate units.
Explanation / Answer
The max acceleration would be, of course, if there were no counter acting friction force. That is impossible; there is always friction. Sometimes it's quite small, but there is always some.
That being said, the max acceleration at theta = 11 deg incline is a = g sin(theta) = 1.87 m/sec^2; where g = 9.81 m/sec^2 and theta = 11 degrees.
I'm guessing 55 long means 55 m long, but you've given us no hints as to the length units. For that matter, you failed to give us the angle units too. For all we know, that might be radians. In any of the sciences, the units are important; use them.
Anyhow V^2 = 2aS = 2*1.87*55 = 205.7 (m/sec)^2 so that V = 14.34 mps at the end of the incline.