Stopping DistanceDate: 02/25/97 at 18:50:59 From: Benjamin Marshan Subject: Physics: momentum A 14700N car is traveling at 25m/s. The brakes are suddenly applied and the car slides to a stop. The average braking force between the tires and the road is 7100N. How far will the car slide once the brakes are applied? All we think we know is that we should be using p = mv. Is this correct? Thank You! Date: 03/07/97 at 18:38:57 From: Doctor Barney Subject: Re: Physics: momentum Instead of giving you the answer, how about I put you on the right track? (Or the right "road", since this is a car problem.) Please write back again if you need more help. Actually, I do not believe that there is enough information given to solve the problem, since it says "average" force. If there is a greater force applied earlier in the braking, the car will stop in a shorter distance. If there is a greater force applied later in the braking, even if the time average of the force is the same and the total time it takes to stop is the same, the car will have traveled a longer distance. Let's assume that the braking force is a "constant" 7100N. I can think of two methods to solve this problem, but neither of them involves momentum, although there may be other methods. 1) Use Newton's second law, F = ma. You know the force and you can find the mass, so you can calculate a constant acceleration (or deceleration, in this case). From the acceleration you can calculate velocity as a function of time. Next integrate the velocity from time 0 (when the brakes are applied) to the time when the car stops moving to find the distance traveled. This is an easy integral since the velocity function is a straight line when the braking force is a constant. 2) Use energy methods. The initial kinetic energy of the car will be equal to the "work" the car does on the tires/road. This equation looks like 1/2mv^2 = Fd where m is the mass of the car, v is the initial velocity, F is the force applied, and d is the distance over which the constant force is applied, which is what you are attempting to determine. Have you covered this yet? Note: With either of these methods, be sure to calculate the mass of the car first, since the problem statement gives you the weight of the car. -Doctor Barney, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 03/07/97 at 18:49:44 From: Doctor Luis Subject: Re: Physics:- momentum You don't really need to consider momentum in this problem. To solve it, let's look at the given information. The weight of the car is 14700N. We can obtain the mass from this: w = 14700 N w = mg m = 14700 N / 9.8 m/s^2 g = 9.8 m/s^2 m = w/g = 1500 kg The average braking force between the tires and the road is 7100 N. We can obtain the deceleration of the car from this: f = 7100 N f = ma a = 7100 N / 1500 kg m = 1500 kg a = f/m = 4.73 m/s^2 The initial velocity of the car (before the brakes are applied) is 25 m/s. Since we know the acceleration of the car and its final velocity (0 m/s - the car comes to a stop), we can calculate the distance traveled by the car as follows: vi = 25 m/s (initial velocity) vf = 0 m/s (final velocity) a = - 4.73 m/s^2 (acceleration) vf^2 = vi^2 +2*a*d Can you take it from here? I hope this helped! -Doctor Luis, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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