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 224 m/s, and its penetration depth was 15 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

200.4 N

Step-by-step explanation:

We start by finding the acceleration acting on the toothpick. Its motion is a uniformly accelerated motion, so we can use the equation

`v^2-u^2=2as`

where

v is the final velocity

u is the initial velocity

a is the acceleration

s is the displacement

In this problem we have

v = 0 (since it comes to a stop)

u = 224 m/s

a = ?

s = 15 mm = 0.015 m is the stopping distance

Solving for a, we find the acceleration

`a=(v^2-u^2)/(2s)=(0-224^2)/(2(0.015))=-1.67\cdot 10^6 m/s^2`

Now, we know that the mass of the toothpick is

`m=0.12 g = 0.12 \cdot 10^(-3) kg`

Therefore, we can find the force exerted on it by using Newton's second law:

`F=ma=(0.12\cdot 10^(-3))(-1.67\cdot 10^6)=-200.4 N`

So, the magnitude of the force is 200.4 N.