Determine the maximum theoretical speed that may be achieved...

Determine the maximum theoretical speed that may be achieved over a distance of $60 \mathrm{m}$ by a car starting from rest, knowing that the coefficient of static friction is 0.80 between the tires and the pavement and that 60 percent of the weight of the car is distributed over its front wheels and 40 percent over its rear wheels. Assume (a) four-wheel drive, $(b)$ front-wheel drive, $(c)$ rear-wheel drive.

Transcript

00:01 We have that.

00:03 We want to determine, so we have this vehicle, and the maximum theoretical speed that can be achieved over 60 meters of a car starting from rest.

00:14 And we have a coefficient of static friction between the tires and the road of the pavement of 0 .80.

00:23 And we also, we're told that there's a weight distribution across here.

00:27 So the weight distribution on the rear wheels is 40 % of the.

00:31 The total weight, so is 0 .4w, and on the front wheels is 60%, so 0 .6w.

00:39 Now, we're told that the vehicle is starting from rest, so we know that the velocity squared equals 2a, the acceleration times the delta x.

00:52 And so in general, we have friction force from the rear wheels and friction force from the front wheels equals a mass times acceleration.

01:02 That tells us that v, solving this for v, and plugging in the equation here for a, we get v is the square root of two times a quantity, 0 .4 mu .s rear plus 0 .4 mus front, front, mu s, front, s, front, s, front, s, front, s, left, x.

01:20 And what i did is i basically just used two different mues here, because they asked us if it was forward drive, frontward drive, or rear road drive.

01:28 So what's going to happen is i'm going to basically say, well, one of these is, or neither of them are zero, depending on the situation, we have the kind of vehicle.

01:38 So if it's four -wheel drive, we know basically both of them are going to be 0 .8 because we have friction forces from both the front and the rear wheels, you know, drive forces.

01:52 And so again, because we're talking about the maximum velocity you could attain over this, the friction force is going to be, the static friction is going to be this maximum.

02:01 So any greater acceleration, if it any greater acceleration, the tires would start to spin...

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