b. Rank the three experiments according to the final kinetic energy of astronaut B, from largest Conservation of momentum in one dimension Mech a. HW-62 to a nearby space station.) After Before Experiments 1, 2, and 3 Pl= 20 kg-m/s At rest At rest The astronauts push on each other in different ways so that the outcome of each experiment is different. As shown in the figure at right, astronaut A has a different final momentum in each experiment. a. Determine the magnitude of the final momentum of astronaut B in each experiment. Explain. IPl=5 kg-m/s 3 dlpl=5 kg-m/s b. Rank the three experiments according to the final kinetic energy of astronaut B, from lar to smallest. Explain. c. Is the total kinetic energy after the collision in experiment 2 greater than, less than, or equal to that after the collision in experiment 3? (In this case, total kinetic energy means the sum of the kinetic energies of the two astronauts.) Explain. 2.

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All of 3 please!
**Conservation of Momentum in One Dimension**

**Scenario Overview:**

Two astronauts, A and B, participate in three collision experiments in a weightless, frictionless environment. In each experiment, astronaut B is initially at rest, and astronaut A has an initial momentum of 20 kg·m/s to the right. The velocities of the astronauts are measured with respect to a nearby space station.

**Diagram Explanation:**

- **Before Collision:**
  - Astronaut A has a momentum \(\vec{p}_{A_i} = 20 \text{ kg·m/s}\) to the right.
  - Astronaut B is at rest.

- **After Collision:**
  1. Experiment 1: Both astronauts are at rest.
  2. Experiment 2: Astronaut A has a momentum \(\vec{p}_{A_f} = 5 \text{ kg·m/s}\) to the left. Astronaut B’s final momentum is unknown.
  3. Experiment 3: Astronaut A has a momentum \(\vec{p}_{A_f} = 5 \text{ kg·m/s}\) to the right. Astronaut B’s final momentum is unknown.

**Questions:**

a. **Determine the magnitude of the final momentum of astronaut B in each experiment. Explain.**

b. **Rank the three experiments according to the final kinetic energy of astronaut B, from largest to smallest. Explain.**

c. **Is the total kinetic energy after the collision in experiment 2 greater than, less than, or equal to that after the collision in experiment 3? Explain.**

d. **Consider the following statement:**

_"The momentum of the system is conserved in each experiment because there is no net force on the system. If momentum is conserved, then kinetic energy must also be conserved, because both momentum and kinetic energy are made up of mass and velocity."_

One of the sentences above is completely correct. Discuss the error(s) in reasoning in the other sentence.
Transcribed Image Text:**Conservation of Momentum in One Dimension** **Scenario Overview:** Two astronauts, A and B, participate in three collision experiments in a weightless, frictionless environment. In each experiment, astronaut B is initially at rest, and astronaut A has an initial momentum of 20 kg·m/s to the right. The velocities of the astronauts are measured with respect to a nearby space station. **Diagram Explanation:** - **Before Collision:** - Astronaut A has a momentum \(\vec{p}_{A_i} = 20 \text{ kg·m/s}\) to the right. - Astronaut B is at rest. - **After Collision:** 1. Experiment 1: Both astronauts are at rest. 2. Experiment 2: Astronaut A has a momentum \(\vec{p}_{A_f} = 5 \text{ kg·m/s}\) to the left. Astronaut B’s final momentum is unknown. 3. Experiment 3: Astronaut A has a momentum \(\vec{p}_{A_f} = 5 \text{ kg·m/s}\) to the right. Astronaut B’s final momentum is unknown. **Questions:** a. **Determine the magnitude of the final momentum of astronaut B in each experiment. Explain.** b. **Rank the three experiments according to the final kinetic energy of astronaut B, from largest to smallest. Explain.** c. **Is the total kinetic energy after the collision in experiment 2 greater than, less than, or equal to that after the collision in experiment 3? Explain.** d. **Consider the following statement:** _"The momentum of the system is conserved in each experiment because there is no net force on the system. If momentum is conserved, then kinetic energy must also be conserved, because both momentum and kinetic energy are made up of mass and velocity."_ One of the sentences above is completely correct. Discuss the error(s) in reasoning in the other sentence.
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