Calculate Force Applied by Tree to Stop 4.5kg Axe at 25 m/s

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In summary: You are quite correct in your interpretation and the steps you took to get as far as you did. I don't think you can do more with them than that.
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physics604
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An airplane has 1.50x10³ m to accelerate to a speed of 62.0 m/s to take off. If it experiences 15,000N of friction, calculate the thrust of the engines.

d=1.50x10³ m
vi=0 m/s
vf=62.0 m/s
Ff=15,000N

v²=u²+2ad
62²=0+2(1.50x10³)a
a=1.2813 m/s²

I think I'm supposed to find the applied force, but I don't know what to do next since I can't find the mass of the airplane.

A 4.5kg axe comes to a stop in a tree from 25 m/s. How much force did the tree exert on the axe?

I couldn't come up with anything for this one:

u=25 m/s
v=0 m/s
m=4.5 kg

ANY HELP IS MUCH APPRECIATED!
 
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  • #2
physics604 said:
An airplane has 1.50x10³ m to accelerate to a speed of 62.0 m/s to take off. If it experiences 15,000N of friction, calculate the thrust of the engines.

d=1.50x10³ m
vi=0 m/s
vf=62.0 m/s
Ff=15,000N

v²=u²+2ad
62²=0+2(1.50x10³)a
a=1.2813 m/s²

I think I'm supposed to find the applied force, but I don't know what to do next since I can't find the mass of the airplane.

A 4.5kg axe comes to a stop in a tree from 25 m/s. How much force did the tree exert on the axe?

I couldn't come up with anything for this one:

u=25 m/s
v=0 m/s
m=4.5 kg

ANY HELP IS MUCH APPRECIATED!

Both questions are missing critical information that would be needed to calculate a numerical answer. Thus the best you can do is to derive symbolic results with the missing information in the form of a variable. In the first case the missing information is the airplane's mass. In the second it's the depth of penetration of the axe into the tree (or perhaps the time for the axe head to come to rest).
 

1. How do you calculate the force applied by a tree to stop a 4.5kg axe at 25 m/s?

In order to calculate the force applied by a tree to stop a 4.5kg axe at 25 m/s, you will need to use the equation F=ma, where F is the force, m is the mass, and a is the acceleration. In this case, the mass is 4.5kg and the acceleration is the change in velocity over time, or 25 m/s divided by the time it takes for the axe to stop. This time can be calculated by dividing the initial velocity (25 m/s) by the acceleration due to gravity (9.8 m/s^2). So, the force applied by the tree would be 4.5 kg * (25 m/s / (25 m/s / 9.8 m/s^2)) = 44.1 N.

2. What is the significance of calculating the force applied by a tree to stop a 4.5kg axe at 25 m/s?

Calculating the force applied by a tree to stop a 4.5kg axe at 25 m/s is important because it allows us to understand the amount of force that is required to stop an object moving at a certain velocity. This information can be useful in determining the strength and stability of trees and other objects in nature, as well as in engineering and design applications.

3. How does the mass of the axe affect the force applied by the tree?

The mass of the axe directly affects the force applied by the tree. According to the equation F=ma, the force is directly proportional to the mass. This means that as the mass of the axe increases, so does the force required to stop it. In this case, a 4.5kg axe would require less force to stop than a heavier axe.

4. What other factors may affect the force applied by a tree to stop an axe?

There are several other factors that may affect the force applied by a tree to stop an axe. These include the velocity of the axe, the type of wood and its density, the angle at which the axe hits the tree, and any external forces acting on the tree (e.g. wind). Additionally, the condition of the tree (e.g. healthy or damaged) may also impact the force required to stop the axe.

5. How can the force applied by a tree to stop an axe be used in real-world scenarios?

The calculation of the force applied by a tree to stop an axe can be used in various real-world scenarios. For example, it can be used in forestry and logging practices to determine the strength and stability of trees when faced with falling objects. It can also be used in the design and testing of tools and equipment, such as axes and tree harvesting machinery, to ensure they can withstand the forces involved. Additionally, understanding this force can also be helpful in assessing the potential damage or impact of falling trees or branches in situations such as storms or accidents.

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