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. Accident analysis. A 1500 $\mathrm{kg}$ sedan goes through a wideintersection traveling from north to south when it is hit by a2200 kg SUV traveling from east to west. The two carsbecome enmeshed due to the impact and slide as one there after. On-the-scene measurements show that the coefficient ofkinetic friction between the tires of these cars and the pave-ment is $0.75,$ and the cars slide to a halt at a point 5.39 $\mathrm{m}$ westand 6.43 $\mathrm{m}$ south of the impact point. How fast was each cartraveling just before the collision?

The speed of the sedan is 21.28 $\mathrm{m} / \mathrm{s}$and the speed of the SUV is 12.16 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 8

Momentum

Physics Basics

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

University of Michigan - Ann Arbor

Hope College

University of Winnipeg

McMaster University

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problem. 8.77. We have two cars a Savannah, a traveling to the South and this SUV be traveling to the West. The masses were given here. They run into each other as cars do and slide together for some distance it along the ground. Now we're told the distance which they slid before together before stopping and given the X and Y components of that displacement. We're told what the coefficient of kinetic friction is between the come combined cars and the ground. And then what we want to do is figure out what we're the what were the speeds of the cars before they had the collusion. So this is going to have two steps. First, we're going to be thinking about energy, and in the second we're going to be thinking about momento. It's a little bit of preliminary here. Um, we want to know what he is. That's easy. We just use the Pythagorean here, um, so is equal to eight points 39 heaters, and we'd also like to know what state it is. Data is the arc tangent of the opposite over Jason sides, and this is about 50 degrees, so little Roman numeral one here. We know that in order to be sliding in the first place, the combined car object had to have some kinetic energy. Will call m a plus envy began and their speed right after they started citing will be just be. And now, in order for this to it stopped some amount of work had to have been done on it. Two You know, it is a kinetic energy. That work was done by friction. So we know the work is the force times the distance over which the forces exerted? No. Then the force of friction is the coefficient of friction. Friends, the normal force which this is. Just wait big anti Miss Jean and then the distance we called the So the speed they're going immediately after the collision is the square root of two coefficient affection, the acceleration of gravity times this distance. They were going 11 0.1 meters per second together right after they hit. Now, in order to use this for the conservation of momentum because it is a vector, we're going to take advantage of the fact we know the initial velocity of a was entirely in the wind direction and the initial velocity of B was entirely in the extraction in order to make our lives easier. This conservation of momentum calculations or are in fact, we need more information we wouldn't have if we didn't know what the directions of you are already. So let's turn our be into a vector before turning our attention to momentum, all we could think of this is the first part of turning our attention for momentum. So this is going to be the magnitude of this and the coastline of the angle the unit vector in the extraction sine of the angle unit vector in the wider erection. And just so we don't have much negative signs that we don't really need, Uh, well, that left b positive extraction and down the positive direction. So you work this out and you find that the velocity vector immediately after the collision, the 7.14 you just for a second and X and 8.5 meters per second and why? Okay, so now the momentum of the combined cars together is the sum of them answers I'm a philosophy just found, and the momento from a will be its mass times its speed times the unit vector in the direction it was going and similarly, for and not just breaking this apart. We'll find the d A is equal to Big M over and a I miss the white component our velocity here and this works out to be 21 meters per second. The speed of the SUV has the same sort of form to the equation because there's nothing special about one or the other in terms of the physics involved. Maybe one of them had a nicer color on the other. There's no way crust No, this was going 12 meters per second. So perhaps the SUV was slowing down and trying not to run a red light and didn't do it in Time Sedan or yeah, who knows what we're not told? But in any event, these air how fast they were going before the collision, and, uh, we worked backwards. Um, what? The results were what the initial conditions were

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