![]() Put in the actual numbers, not (for example) F = ma for the deceleration force. You will have to decide if simple is good enough, or if you need to be correct. Assuming that tire normal force is the same at both constant speed and heavy braking simplifies the calculations, but is not correct. The total braking force, of course, is equal to ma. This will be the actual braking force in a properly balanced brake system, or a brake system with a working antilock system. The maximum braking force of each tire is proportional to the tire normal force. If you take a sum of moments about either tire contact patch in the whole car FBD, you will find that the tire normal force is not 210/160 kg. If the wheel locks up, then you will have extra internal forces acting on your caliper (but not at the tire) if the driver pushes harder on the pedal (your first equation, without the #\frac\times 2 \times coef\ of\ friction#). In any circumstance, as long as the wheels turn, the maximum force will be dictated by the tire friction force (your second equation). The logical conclusion from looking at those results is that the braking system requires less brake pedal force to achieve the desired tire performance. The second equation is evaluating what force is required by the tire (which should be based on the tire friction force the deceleration will be govern by the friction force).The first equation is evaluating what force the braking system can produce based on the brake pad friction force.The #F = 70332.32 N# of the first equation is actually equivalent of the #F_w# of the second equation for one wheel (i.e. When the brakes break, it does not slow down.Īlthough two completely different solutions, should both not be of similar value? Are my calculations correct for either of the solutions? Or if in fact they are does anyone know why they are so different? Many times it is helpful to add a note to the FBD stating exactly what you are supposed to find.ģ) Always label your answers with what the number represents: Vehicle speed, vehicle deceleration rate, braking force at the road, braking force at the caliper, caliper squeezing force, etc.Ĥ) A vehicle acceleration of 15 m/sec^2 is truly impressive.ĥ) When the brakes brake, the vehicle slows down. Then, and only then, think about what equation(s) relate what you know to what you want to find. It needs to include all given information - weight, acceleration, etc.Ģ) Think carefully about what information you are given, and what you are trying to find. The diagram can be a simple pencil sketch. Rather than give you the answer (this sure looks like a homework problem), I'll give you some hints:ġ) Always start a problem like this with a free body diagram (FBD). In this case, you got two different answers because you solved two different problems. You are doing the right thing when you cross check your work. ![]()
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