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?

200.4 N

Explanation:

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

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

Now, we know that the mass of the toothpick is

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

So, the magnitude of the force is 200.4 N.

the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm