Tree Cutting Word Problem: Why Does the Short Tree Hit the Ground First?

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.
  • #1
physicsgurl12
184
0

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?
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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?
 
  • #5
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.
 

What is the tree cutting word problem?

The tree cutting word problem is a mathematical problem that involves determining the number of cuts needed to cut down a tree with a given height, based on a set of rules and restrictions.

What are the main factors that affect the solution of the tree cutting word problem?

The main factors that affect the solution of the tree cutting word problem include the height of the tree, the maximum height that can be cut with each cut, the maximum number of cuts allowed, and any other constraints or rules specified in the problem.

What is the most efficient way to solve the tree cutting word problem?

The most efficient way to solve the tree cutting word problem is by using a systematic approach, such as creating a table or diagram to organize the information and determine any patterns or rules, and then using algebraic equations to find the solution.

What are some real-life applications of the tree cutting word problem?

The tree cutting word problem has various real-life applications, such as in forestry and logging industries, determining the number of cuts needed to fell a tree in a controlled manner, and in manufacturing and production processes that involve cutting materials to specific lengths.

What are some common misconceptions about the tree cutting word problem?

One common misconception about the tree cutting word problem is that the number of cuts needed is always equal to the height of the tree. However, this is not always the case as the maximum height that can be cut with each cut is a limiting factor. Another misconception is that the number of cuts needed is always an integer, but in some cases, fractional cuts may be allowed.

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