@ One object is at rest, and another is moving. The two...

@ One object is at rest, and another is moving. The two collide in a one-dimensional, completely inelastic collision. In other words, they stick together after the collision and move off with a common velocity. Momentum is conserved. The speed of the object that is moving initially is 25 $\mathrm{m} / \mathrm{s}$ . The masses of the two objects are 3.0 and 8.0 $\mathrm{kg}$ . Determine the final speed of the two-object system after the collision for the case when the large-mass object is the one moving initially and the case when the small-mass object is the one moving initially.

@ One object is at rest, and another is moving. The two collide in a one-dimensional, completely inelastic collision. In other words, they stick together after the collision and move off with a common velocity.
Momentum is conserved. The speed of the object that is moving initially is 25 $\mathrm{m} / \mathrm{s}$ . The masses of the two objects are 3.0 and 8.0 $\mathrm{kg}$ . Determine
the final speed of the two-object system after the collision for the case when the large-mass object is the one moving initially and the case when the small-mass object is the one moving initially.

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Key Concepts

Conservation of Momentum

Conservation of momentum is a fundamental principle in physics stating that in an isolated system, where no external forces are acting, the total momentum remains constant before and after an event such as a collision. In collision problems, this principle allows us to relate the initial momenta of colliding objects to their final momenta, regardless of the nature of the collision.

Completely Inelastic Collision

A completely inelastic collision is a type of collision in which the colliding objects stick together after impact and move with a common velocity. In these collisions, while momentum is conserved, kinetic energy is not conserved due to energy losses from factors like deformation or sound, making the analysis rely solely on momentum conservation principles.

Transcript

00:01 And this problem there are two masses.

00:03 One is three kilograms.

00:05 We'll call that m1, and the second one is eight kilograms.

00:11 We'll call that one m2.

00:13 And the collision that occurs in this problem is completely inelastic.

00:17 So they stick together after the collision.

00:20 So we know that our equation for momentum will be p initial or p not is equal to p final.

00:27 So we have the two things separate, the two objects.

00:33 Initially will then combine to make one mass because they stick together and they have a final velocity of the f.

00:42 So in this problem they ask us to analyze the case for two certain cases.

00:49 We know that the velocity of whichever one is moving is 25.

00:52 Call that be not.

00:54 But they ask us to solve it for when the heavy object is moving at that speed and for when the light object is moving at that speed.

01:02 So let's start with the heavy object, the eight kilograms.

01:06 So if eight kilogram mass is moving, oops, if the eight kilogram mass is moving at 25 meters per second, we called our eight kilogram mass m2, so that would be v2.

01:29 So we would say that m1 would be three kilograms.

01:34 The initial velocity of the light mass is going to be zero, and the other mass is eight kilograms, and its velocity is 25...

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