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Learning Introductory Physics with Activities

Section 9.8 Challenge - Momentum

Subsection Explanation Tasks

Explanation 9.8.1. Colliding Astronauts.

Two astronauts, Michael and Collins, conduct several collision experiments in an environment with no external forces. Michael has a larger mass than Collins. In each experiment, Michael is initially moving with speed \(v_i\) in the positive \(x\)-direction and Collins is initially at rest.
  • In case A, Michael’s final velocity is \(0\text{.}\)
  • In case B, Michael’s final velocity is \(\frac{v_i}{4}\) in the negative \(x\)-direction.
  • In case C, Michael’s final velocity is \(\frac{v_i}{4}\) in the positive \(x\)-direction.
Rank the experiments by Collins’ final kinetic energy.
Tip.
Sketch a momentum vector diagram for each case.

Subsection A*R*C*S Activities

A*R*C*S 9.8.2. The Exploding Firecracker.

You throw a firecracker vertically upward. At \(t = 0\text{,}\) the firecracker is moving upward with speed \(v_1\text{,}\) at which point it begins to explode, splitting into an upper piece with mass \(m_u\) and a lower piece with mass \(m_l\text{.}\) The explosion finishes at \(t = \frac{v_1}{g}\text{,}\) at which point you observe that the upper piece is still moving upward with speed \(3v_1\text{.}\)
Determine the velocity of the lower piece at \(t = \frac{v_1}{g}\text{.}\)
Tip 1.
For your representation (part 1c), sketch a momentum vector diagram.
Tip 2.
For your symbolic sensemaking (part 3c), try at least two special cases.

Activity 9.8.3. Metacognitive Reflection.

In studying energy and momentum, you learned about conservation laws, which provide a different perspective on the world than forces do. Summarize the conservation laws you learned about, including information about when each quantity is conserved.