Question

The high-speed winds around a tornado can drive projectiles into trees, building walls, and even metal traffic signs. In a laboratory simulation, a standard wood toothpick was shot by pneumatic gun into an oak branch. The toothpick mass was 0.12 g, its speed before entering the branch was 221 m/s, and its penetration depth was 16 mm. If its speed was decreased at a uniform rate, what was the magnitude of the force of the branch on the toothpick?

Answer 1

F = 183.153 N

Step-by-step explanation:

given,

mass of the toothpick = 0.12 g = 0.00012 kg

initial velocity = 227 m/s

final velocity = 0 m/s

penetration depth = 16 mm = 0.016 m

using the equation of motion

v² - u² = 2 a s

0 - u² = 2 a s

- 221² = 2 × a × 0.016

a = 1526281.25 m/s²

Force is equal to

F = m a

= 0.00012 × 1526281.25

F = 183.153 N