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winowmak3r
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Homework Statement
I'm having a real hard time on the last homework question for this week for my Uni Physics I course. Here it is:
Top-fuel dragsters can accelerate from rest at a rate of about 5g. If this does not sound impressive, consider that for most automobiles the friction between the ground and the tires produces the acceleration. Since the coefficient of friction between regular treaded tires and pavement is typically less than or about equal to 1.0, a car relying on friction with normal force equal to its weight should accelerate at no more than about 1g.
Dragsters use two methods to increase their acceleration. First, they greatly increase the friction between their tires and the road by eliminating tire tread (dragsters do not race in wet or snowy road conditions) and also by performing a “burnout” which lays down a patch of heated rubber on the track that the partially-melted tires will adhere to. The result of these measures is a coefficient of friction exceeding 2.0. The second important method for increasing acceleration is the use of engine exhaust to provide force. The high-speed exhaust gases exiting the dragster’s enormous 8000 hp engine produce a force with a size comparable to the car’s weight.
a.) Assuming a coefficient of friction equal to 2.5, at what angle θ measured with respect to the horizontal (bottom picture) should the exhaust pipes be oriented in order to achieve maximum acceleration? Assume the engine is capable of using the tires to produce a force equal to the maximum friction force (μN) regardless of how large the normal force becomes!
θ
b.) Supposing the coefficient of friction is 2.5 and the exhaust is configured at the optimal angle found in part (a), how much force (as a fraction of the dragster’s weight) would the exhaust have to produce if the dragster accelerates from rest at 4.7g?
Homework Equations
F=m*a
F(friction)=uN
W=F*r*cos(theta)
More?
The Attempt at a Solution
I honestly have no idea. The correct answer for part a is 68 degrees (After much coercing the professor gave us the answer to part a but wouldn't tell us how to get there yet). A friend and I tried to do this problem and came up with 0 degrees but the logic was pretty shaky. Basically we reasoned that if u is 2.5, and the normal force is m*g*cos(theta) then you would want cos(theta) to be 1, hence zero degrees.
Any help is much appreciated!