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

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The discussion centers on calculating the force exerted by a tree to stop a 4.5 kg axe traveling at 25 m/s. The key formula used is the impulse-momentum theorem, which relates the change in momentum to the force applied over time. The missing variables, such as the depth of penetration of the axe into the tree or the time taken to stop, prevent a numerical answer from being derived. Additionally, a parallel question regarding the thrust of an airplane experiencing friction is also discussed, highlighting the importance of knowing the airplane's mass for accurate calculations.

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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!
 
Last edited:
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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).
 

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