An automobile with a mass of 980kg is moving with a constant...

An automobile with a mass of 980 kg is moving with a constant velocity of 44.8 mi/h (1 m/s = 2.24 mi/h) on a straight level road. The driver sees a construction barrier ahead and applies the brakes. The frictional force between the tires and the road is equal to 1/2 the weight of the vehicle. How far will the vehicle travel before it comes to a complete stop? a) Complete a vector diagram of the situation. Show weight, normal force, and distance to stop point (displacement). b) Show a working equation based on the work/energy relationship that can be used to find the stopping distance. Start with the equation W = Î”KE. c) Calculate the distance it will take to stop the automobile.

Transcript

00:01 Okay, so we've got a car that's coming to a stop here, and we want to first draw a diagram of this.

00:05 So for part a, we'll say, you know, the car has an initial velocity, 44 .8.

00:14 This is in miles per hour.

00:17 And then a final velocity of zero with the displacement d.

00:24 They want us to draw the normal force and weight of the vehicle, and then i would draw friction as well.

00:32 You're going to have the weight, which is equal to mg, normal, which is equal to mg, and then force friction, which is slowing it down.

00:41 So this is what i would do for the diagram here.

00:46 We want to show an equation that relates work and energy.

00:50 Okay, so in order to do this, let's give you a little space here.

00:56 Okay, so work is equal to the change in kinetic energy.

00:59 So k e final minus k e initial okay so work is going to be equal to one half mv final squared and then the initial kinetic energy you know what i take this back i did this backwards sorry so it has kinetic energy initially there's no final so the final is actually going to be zero because it comes to a stop okay so work is going to be equal to negative of the original kinetic energy.

01:39 They give us that the mass is 980 kilograms, and the speed is given, but we need to convert it into meters per second.

01:48 So let's go ahead and do that now.

01:51 Okay, so coming back over here, 44 .8 miles per hour, and they gave us a conversion factor.

02:01 One meter per second is 2 .24 miles per hour.

02:09 Okay, so we're going to divide by 2 .24.

02:16 And that gives us 20 meters per second.

02:20 Nice even number there.

02:23 Okay, so let's get back to where i was.

02:27 Sorry, here my screen is giving me a little trouble...