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Two bumper cars in an amusement park ride collide elastically as one approaches the other directly from the rear (Fig. 56). Car A has a mass of 450 $\mathrm{kg}$ and car $\mathrm{B} 490 \mathrm{kg},$ owing to differences in passenger mass. If car A approaches at 4.50 $\mathrm{m} / \mathrm{s}$ and car $\mathrm{B}$ is moving at 3.70 $\mathrm{m} / \mathrm{s}$ , calculate $(a)$ their velocities after the collision, and (b) the change in momentum of each.

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Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Cornell University

University of Washington

Hope College

University of Winnipeg

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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Two bumper cars in an amus…

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(II) Two bumper cars in an…

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07:43

At an amusement park there…

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Two bumper cars moving on …

02:30

In an elastic collision, a…

the fact that this is an elastic collision on DSO for an elastic collision. Um, you're the difference from your initial velocity, Zvi. A minus you. Beauty is equal to the negative of the difference between the final velocities. Ah, via prime CB front. So you have here that BB prime? Is it cool to be a minus? Beauty plus V a prime. And so this is Ah, Via is 4.5 aa minus baby 3.7 plus v a prime. So, Bebe is there 4.8 Plus he a prime meters per second. Therefore from momentum conservation, we have obviously a v A plus m b b initial Momenta is equaled. Final memento, eh? Maybe a prime plus m b B B prime and so Vehbi prime is 0.8 times v a prime. Therefore, in writing things down in terms of being a prime, we have v a prime, uh, Times M A plus m b is equal to m a v a plus m beauty times, point times Ah v B minus 0.8. Okay, um and so v a prime therefore, is ah m a v A plus and B times V b minus 0.8 over M A plus M b. Okay, and therefore V A prime is just, um is 4 50 kilograms, turns 4.5 meters per second. Uh, plus for 90 kilograms turns 2.9 meters per second. Uh, over 4 50 plus 4 90 uh, kilograms. So v a prime is 3.67 meters per second. Ah, therefore Avi be prime. It's this plus 0.8. So this is 0.8 plus 3.67 calls 4.47 meters per second. All right. And in part B, we're just calculating the change in momentum. Eso for air you have dealt appear is an eight times V a minus b a prime change in velocity stars must So this is 4 50 kilograms times 3.67 67 minus 4.5 meters per second, giving Delta P A of negative 3 75 kg meters per second. Ah, and similarly, for a Delta P B, you have m b times B B minus V b prime and so that's 4 90 kilograms times 4.47 minus, uh, 3.7 uh meters per second, Right Similar to here. Uh, and so this gives us to be 75 kilograms meters per second. Note that Delta Pew B is equal and opposite to Delta Pier, which means the momentum is conserved.

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