Question

I Three objects A,B, and C are moving as shown in Figure 8.37. Find the x and y components of the net momentum of the particles if we define the system to consist of (a) A and C, (b) B and C, (c) all three objects. Figure 8.37 Problem 3.

Answer 1

(a) The x-component of the net momentum of A and C is 16 kg m/s, and the y-component is 0 kg m/s.

(b) The x-component of the net momentum of B and C is -24 kg m/s, and the y-component is -8 kg m/s.

(c) The x-component of the net momentum of all three objects is -8 kg m/s, and the y-component is -8 kg m/s.

Step-by-step explanation:

When considering the x and y components of momentum for the pairs of particles:

(a) For A and C, the x-components add up as both have positive momentum in the x-direction (8 kg m/s + 8 kg m/s = 16 kg m/s), while in the y-direction, they both have zero momentum, resulting in 0 kg m/s as the net y-component.

(b) Considering B and C, their x-components result in a subtraction (0 kg m/s - 24 kg m/s = -24 kg m/s) due to B's negative momentum in the x-direction. In the y-direction, C's momentum (-8 kg m/s) subtracts from B's momentum (-8 kg m/s), yielding a net y-component of -8 kg m/s.

(c) When accounting for all three objects, their x-components combine (16 kg m/s - 24 kg m/s = -8 kg m/s) and the y-components add up (-8 kg m/s + (-8 kg m/s) = -16 kg m/s), resulting in -8 kg m/s for both x and y components of the net momentum.

This analysis demonstrates how combining the momenta of different pairs of objects in the x and y directions provides the net momentum of the specified groups.

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Answer 2

To find the x and y components of the net momentum of the particles, break down the momentum vectors into their x and y components and add them separately.

Step-by-step explanation:

To find the x and y components of the net momentum of the particles in the system, we can break down the momentum vectors into their x and y components. We can then add the x and y components separately to obtain the x and y components of the net momentum for each combination of objects.

For example, for system (a) consisting of objects A and C, we add the x components of their momentum vectors to obtain the x component of the net momentum, and we add the y components to obtain the y component of the net momentum.

This process can be repeated for system (b) consisting of objects B and C, and for system (c) consisting of all three objects. By calculating the x and y components of the net momentum for each system, we can determine the magnitude and direction of the net momentum for each system.