A car of mass m 1120 kg is traveling down a 14 degree...

A car of mass m = 1120 kg is traveling down a θ = 14 degree incline. When the car's speed is v0 = 16 m/s, a mechanical failure causes all four of its brakes to lock. The coefficient of kinetic friction between the tires and road is μk = 0.45. Write an expression for the magnitude of the force of kinetic friction, Fk. Write an expression for the magnitude of the change in the car's height, h, along the y-direction, assuming it travels a distance L down the incline. Calculate the distance the car travels down the hill L in meters until it comes to a stop at the end.

Transcript

00:02 A car of mass 1 ,120 kilograms is traveling down a 14 degree incline.

00:08 When the car speed is 17 meters per second, a mechanical failure causes all four of its brakes to lock.

00:14 The coefficient of kinetic friction by the tires on the road is 0 .45.

00:18 We want to write an expression for the magnitude of the kinetic friction force.

00:30 Let's show an illustration help us solve our problem.

00:42 So we have our car traveling down the incline.

00:52 That is inclined by theta equal to 14 degrees.

00:56 I'll just write theta.

01:01 Let's start by drawing our forces involved.

01:05 So we have mg pointing downwards.

01:09 The normal force, the incline, in a perpendicular direction.

01:16 And we have the force of friction.

01:26 And these kinds of problems is easier to incline our cartesian grid.

01:35 So let's start by finding our expression for the the friction force, so friction is given by the product of the kinetic, by the coefficient of friction, in this case kinetic, because the car is moving, times normal force.

01:53 To find normal force, we're going to sums our forces along the y direction.

01:57 These must be equal to zero because our car isn't lifting.

02:01 Now what we find is that n is equal to mg coast data.

02:08 This angle right here is theta.

02:20 So we find that our friction force writes as uk, mg coast data.

02:35 Next we want to write an expression for the change and the car is height along the y direction...