Is Sliding Down a Falling Tree Safer Than Free Falling?

[taloz]

Homework Statement

A person is atop a tree as it is cut down. Should he push off from the tree and fall freely to the ground or hold on and ride the tree to the ground?It would be a good idea to lay down some physics formulas to support your argument.

Homework Equations

F=ma
Torque = I*Angular Acceleration

angular acceleration = V^2 /r

The Attempt at a Solution

My teacher told our class that we should look at the force acting on the person as they fall.

I know that in free fall the force acting on the person would be (9.8*mass) Newtons because F=ma and a= -9.8 m/s.

With that said, I'm very confused as to how to find the force acting on a person as they accelerate in rotational motion. The reason for this is that i know that the force of gravity is a torque that makes the tree-- and the person attached to it-- fall faster. However, the torque due to the force of gravity should change as the tree falls further and further down. because of this, i don't know how to calculate how much force the person has acting on him/her.

As a note, my teacher has told me that it is 1.2 times more dangerous to hold on to the tree-- i know that free falling is safer-- but wants my class to show the logic and work that brings us to this conclusion. I'm utterly lost.

 

[fizzynoob]

torque = R X F = I*w

since force is acting perpendicular to the branch it can be rewritten as

R*F = I*w

 

[taloz]

But, without using numbers and just variables, how can i quantify the force of I*w/R in terms of just mass as i use 9.8*m as the force of the other one?

I don't have any numbers to use here, nor do i know the moment of inertia in this situation.

also, isn't torque = I* angular acceleration not I * the angular velocity?

 

[taloz]

can anyone help me please? My teacher's question is not phrased very well so i don't understand how to go about solving it.

 

[bobbyrob91]

It's a trick question. The person should slide down the tree like a firepole.