Solve for Impact Speed of 0.25kg Pine Cone Falling 20m

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In summary, a 0.25 kg pine cone falls from a branch 20 meters above the ground. If air resistance is ignored, it would hit the ground with a speed of 6.9 m/s. However, if it actually hits the ground with a speed of 9.0 m/s, the average force of air resistance on it would be 2.45 J.
  • #1
get_rekd
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A 0.25 kg pine cone falls from a branch 20 meters above the ground.

a) What speed would it hit the ground if the air resistance could be ignored?

I am not too sure how to do this but this is what I've got so far:

m=0.25
g=9.8 m/s^2
F=2.45 J
h=20 m

Ep=(0.25kg)(9.8m/s)(20m) Ek=1/2mv^2
=4.9J 4.9J=1/2(0.25kg)(v^2)
2(4.9J=1/2(0.25kg)(v^2))
9.8J=(0.25kg)(2v^2)
-0.25 -0.25
9.55J=2v^2
------------
2
4.775 = v^2
root 4.775 = 2.2 m/s = v ?

is this even close to correct. I think I am doing something wrong
 
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  • #2
right method...check your calculations
 
  • #3
I am also not sure in my calculation of Potential Energy wether
Ep=(0.25kg)(9.8m/s^2)(20m)
= 4.9 or 49
 
  • #4
get_rekd said:
A 0.25 kg pine cone falls from a branch 20 meters above the ground.

a) What speed would it hit the ground if the air resistance could be ignored?

I am not too sure how to do this but this is what I've got so far:

m=0.25
g=9.8 m/s^2
F=2.45 J
h=20 m

Ep=(0.25kg)(9.8m/s)(20m) Ek=1/2mv^2
=4.9J 4.9J=1/2(0.25kg)(v^2)
2(4.9J=1/2(0.25kg)(v^2))
9.8J=(0.25kg)(2v^2)
-0.25 -0.25
9.55J=2v^2
------------
2
4.775 = v^2
root 4.775 = 2.2 m/s = v ?

is this even close to correct. I think I am doing something wrong

Ep=(0.25kg)(9.8m/s)(20m) Ek=1/2mv^2
=49J 49J=1/2(0.25kg)(v^2)
2(4.9J=1/2(0.25kg)(v^2))
98J=(0.25kg)(2v^2)
-0.25 -0.25
97.75J=2v^2
------------
2
48.87 = v^2
root 48.87 = 6.9 m/s = v ?
Would this be correct then?
 
Last edited:
  • #5
looks good...answer makes more sense
 
  • #6
Thanks a lot!
 
  • #7
So there is a part B to the problem:

If it actually hits the ground with a speed of 9.0 m/s, what was the average force of air resistance on it?

Since I got a velocity of 6.9 m/s with 0 air resistance in the first part of the problem wouldn't there be some force accelerating this cone in this part? Because a falling cone with air resistance should hit the ground slower than a cone with no air resistance?
 
  • #8
watch your algebra in part (a)
 
  • #9
Is it still wrong? I cannot seem to find where I made a mistake? Which section of the calculation?
 

1. How do I calculate the impact speed of a falling pine cone?

To calculate the impact speed of a falling pine cone, you will need to use the formula v = √(2gh), where v is the impact speed, g is the acceleration due to gravity (9.8 m/s²), and h is the height from which the pine cone falls (20m in this case).

2. What is the mass of the pine cone?

The mass of the pine cone is given as 0.25kg in the question.

3. How do I convert the height from meters to centimeters?

To convert from meters to centimeters, you can multiply the height (20m) by 100, since there are 100 centimeters in 1 meter. This would give you a height of 2000cm.

4. What is the unit of measurement for impact speed?

The unit of measurement for impact speed is meters per second (m/s).

5. Can this formula be used for objects other than pine cones?

Yes, this formula can be used to calculate the impact speed of any object that falls from a given height. However, keep in mind that this formula assumes that the object is falling in a vacuum, with no air resistance. In real-world scenarios, air resistance may affect the impact speed.

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