Five objects have the same initial speed of 10 meters per...

Five objects have the same initial speed of 10 meters per second. After striking a wall, some of them are stopped and some of them bounce back with varying speeds. Which object experiences the greatest change in momentum? (A) A 1.0 kilogram mass stopping. (B) A 1.0 kilogram mass bouncing back at 10 meters per second. (C) A 2.0 kilogram mass stopping. (D) A 2.0 kilogram mass bouncing back at 5.0 meters per second. (E) A 2.0 kilogram mass bouncing back at 10 meters per second.

Five objects have the same initial speed of 10 meters per second. After striking a wall, some of them are stopped and some of them bounce back with varying speeds. Which object experiences the greatest change in momentum?
(A) A 1.0 kilogram mass stopping.
(B) A 1.0 kilogram mass bouncing back at 10 meters per second.
(C) A 2.0 kilogram mass stopping.
(D) A 2.0 kilogram mass bouncing back at 5.0 meters per second.
(E) A 2.0 kilogram mass bouncing back at 10 meters per second.

Key Concepts

Impulse

Impulse is the change in momentum resulting from a force acting over a period of time. It connects the force applied during an impact with the resulting change in the object's momentum, making it a crucial concept in collision analysis.

Momentum

Momentum is a vector quantity defined as the product of an object’s mass and its velocity. It represents the quantity of motion an object has, and changes in momentum are central to understanding how objects interact, especially during collisions or impacts.

Vector Quantities

Since momentum is a vector, both its magnitude and direction are important. A change in the direction of an object’s motion, as seen when it bounces back from a collision, can significantly affect the total change in momentum even if the speeds before and after remain similar.

Transcript

00:01 Okay, so today we're going to talk about the linear momentum.

00:03 So the linear momentum of a particle in a horizontal motion.

00:07 So this is the surface, and here we have a particle.

00:12 So the linear momentum of this particle that has a velocity v and a mass m is going to be equal to the mass times the velocity.

00:24 And the limit momentum is a vector quantity, okay? now, in this exercise, let's suppose that we have five balls moving in a horizontal surface.

00:37 Here i'm going to draw only two of them, so the drawing does not become too crowded.

00:43 And we know that all balls have the same initial velocity.

00:49 I'm going to write here, v0, and it's equal to 10 meters per second.

00:54 Okay, the balls have different masses.

00:56 And we know that eventually these balls are going to strike in a wall.

01:07 And after striking the wall, some of these balls are going to be stopped.

01:12 So we'll have a final velocity vf equal to zero.

01:18 And some of these balls are going to gain velocity to the other direction.

01:28 Okay? now, given this, we want to find which one of the balls are going to have the largest variation in the linear momentum.

01:42 Okay? the first scenario that we have, the first ball, the exercise tells us a ball of one kilogram, and this ball will strike the wall and will be stopped it.

02:01 Vf will be equal to zero for the first ball.

02:05 So what is going to be the change in the linear momentum? so the change in the linear momentum will be the initial, sorry, the final linear momentum minus the initial linear momentum.

02:18 I'm going to call v0.

02:20 Okay? we know that the final velocity is going to be zero.

02:28 So this term will be zero, such that the variation, will be just minus the mass, so 1 times 10 meters per second.

02:40 And since the velocity initially will point to the right, the velocity is positive, so minus 1 times 10 meters per second.

02:54 So the variation will be minus 10, newton's time second...

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