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You have been hired as an expert witness in a court case involving an automobile accident. The accident involved car A of mass 1500 $\mathrm{kg}$ which crashed into stationary car $\mathrm{B}$ of mass 1100 $\mathrm{kg} .$ The driver of car A applied his brakes 15 $\mathrm{m}$ before he skidded and crashed into car B. After the collision, car $A$ slid 18 $\mathrm{m}$ while car $\mathrm{B}$ slid 30 $\mathrm{m}$ . The coefficient of kinetic friction between the locked wheels and the road was measured to be $0.60 .$ Show that the driver of car A was exceeding the $55-\mathrm{mi} / \mathrm{h}(90 \mathrm{km} / \mathrm{h})$ speed limit before applying the brakes.

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The car was overspeeding 70 \mathrm{mi} / \mathrm{h}

Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Sheffield

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

03:47

In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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because we're doing Chapter nine. Probably. I hear. So it says you've been hired as an expert witness in a court case in an automobile accident. We have a car A with a mass of 1500 kilograms. We crashed into a stationary car e Mass. 1100 kilograms. Something is also that the be initially zero here, the driver of car Eddie of White, his brakes 15 meters before he skidded into the car. So don't the ex breaks is 15 years before he skated after after the collision car A slid. So don't the ex sly because 18 meters or carby out X B slid 30 meters, says the coefficient of kinetic friction between the lock wheels on the road. I was given the 0.6 show that driver A was exceeding 55 miles per hours implements before the brakes. Okay, so this is a lot of stuff going on, but the key is you need to first figure out the speed of the cars immediately after the collision. Bye. See figuring out how far they slot using the work energy. Zero. Next, we will use momentum conservation to figure out the speeds before the collision more of the speed of the car colliding before the collision. And then we use the work energy theory and one more time to get to speak or apply the brakes. Okay, now, so work Energy theorem says that the work from friction it's gonna be the change in kinetic energy. That's 1/2 in the final square, minus B squared. Now the work from friction is done by negative kinetic energy times the normal force times the distance who or negative kinetic coefficient times mg Doctor. Thanks. Okay, so now these IMS can cancel out here. We console for velocities of both after the collision. Wait. Get that by rearranging these for five gold velocities. Sorry, this is the final velocities are zero about these case, the initial velocities of what we're solving for because this is the initial meaning. Right after new craft or wreck. Lucien go. So when we rearrange that setting the F 20 in these cases, this becomes the square root of two Jr Delta X. How much they slide okay to G. Delta acts. So for a it's becomes square root of two times 0.6 time 9.8, and that slit 18 meters you teen years that comes out to be 14 points 55 meters per second. Same calculation. Here is two times you report 69.8 for 9.8 times 30 years. Of course bones to its initial speed after the crash as 18.78 news per second. Okay, so now since we know that momentum is conserved joined during the collision initial moment and was in a b A and then the final was in a be a prime plus in a and the B prime. So if we saw this for the initial speed of a So the speed right before the collision of a now express as a prime cause and he the b crime over Hey, so now we can get the speed right before the collision off car, eh? So spoke the same 1500 times 14 or 55 plus 1100 terms, 18.70. Divide this by 1500 looking or calculator and you get 28 in two years per second. So that's how fast he was After applying the great breaks right before hitting a stationary car, we want to figure out how fast he waas going before applying brakes to do. To do that, we're going to use work energy zero again and said, Negative UK terms G terms the spray Kes distance, and this is equal to the change in Connecticut. Be a squared minus the initial square. Okay, so if we solve this for the initial find, this is a square root of the A squared Maya to Yu gi. Doctor X pregnant 28 court 32 squared minus two times 0.6 times 9.8 times 15 meters. We solved that out. We get 31.23 meters per second. Okay, so the speed limit was 55 miles per hour. So convert that over everyone quarter to three years per 2nd 1 over 0.4. Force is the conversion factor. It's rough. 70 miles per hour. So this person was definitely speaking cool.

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