# Tree cutting word problem

• physicsgurl12
In summary, a tall tree and a short tree of the same mass density and width are cut at the base at the same time. The small tree hits the ground first because the top of the tree has to move a shorter distance compared to the taller tree. The problem can be solved using a free body diagram and conservation of energy, but the initial angle and speed of the tree must be known to find a quantitative answer. It is important to understand the relevance of equations in solving word problems.

## Homework Statement

a tall tree and a short tree of the same mass density and width are cut at the base at the same time. why does the small tree hit the ground first?

## Homework Equations

none. its a word problem

## The Attempt at a Solution

gravity id pushing in different ways?

simple hint: How far does the top of the tree have to move for a small and for a large tree? could a tree that's twice as tall move twice as fast?

harder: replace the tree with a pole with length l. suppose it's at an angle A from the vertical. Draw a free body diagram and find all the forces. You could also find the speed at angle A with conservation of energy. Solve the differential equation for the movement of the tree. (probably needs to be done numerically)
A problem is what the initial angle, or the initial speed of the tree would be.

saying that a word problem has no relevant equations is just silly. If there are no equations, then you are not going to get any answer.

phinds said:
saying that a word problem has no relevant equations is just silly. If there are no equations, then you are not going to get any answer.

really? because the answer above you helped me and they didnt use any equations?

physicsgurl12 said:
really? because the answer above you helped me and they didnt use any equations?

Yes, you're right, of course. I should have said, you won't get a quantitative answer. You'll notice that willem DID talk about equations. To really understand what's going on, you need the math.

EDIT: And it IS silly to say that a word problem has no equations. If you don't understand that, you aren't going to get far in answering word problems.