Question

If Burt's mass increases, the number of snowmen destroyed

If Burt's speed increases, the number of snowmen destroyed

Answer 1

Short answer: both increase the number of snowmen Burt can destroy, but speed has a stronger effect because kinetic energy depends on v^2 while it depends only linearly on mass.

Explanation and simple model
- Useful quantity: kinetic energy KE = 1/2 · m · v^2. If each snowman requires, on average, an amount of energy E0 to destroy, a rough upper bound on how many snowmen Burt could destroy is
N ≈ (1/2 · m · v^2) / E0.
- Consequences:
- If you increase Burt’s mass m while keeping speed v constant, KE and therefore N increase proportionally to m (double m → about double N).
- If you increase Burt’s speed v while keeping mass m constant, KE and N increase with v^2 (double v → about four times N).

Other relevant effects
- Momentum p = m·v matters too for pushing through sequential collisions; higher momentum makes it easier to continue after each impact.
- Real collisions are not perfectly efficient: energy is lost to deformation, sound, heat, and the motion of broken snow, so the actual number will be less than the ideal KE/E0 prediction.
- Geometry, snow cohesion, friction, and how collisions occur (one-at-a-time vs. bunching) strongly affect results; the simple KE model is only an order-of-magnitude estimate.

If you want, give me Burt’s mass and speed (or E0), and I’ll compute a numeric example.