Effective Weight of Falling Object

In summary, the effective weight of a branch that falls from a tree to the ground is determined by its increased speed as it falls. The mass of the branch remains the same, but its kinetic energy increases as it falls. The energy of an object falling from a height can be calculated using the formula E = (9.8m/s^2)mh. To calculate the velocity of the branch, the formula v = √(2gh) can be used. This does not take into account air resistance or the weight of the leaves, but can provide a theoretical value. The weight of the branch can be calculated using the formula F = ma, assuming a deceleration time of 0.3 seconds.
  • #1
damon
1
0
I'm am trying to determine the effective weight of a branch that falls from a tree to the ground. When I say the "effective weight" I mean the effect of the increased speed of the branch as it falls.

The branch would fall from say 30 metres (say 90 feet) and would initially weigh 1 kilgrams (say 2.2 pounds).

I'd appreciate either the answer or a formula to work it out. BTW, I'm not a student we are just fighting our local Council (in Sydney) to remove a tree! They think the branches are small but when they hit they hurt!

Thanks in advance for any assistance.

Damon
 
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  • #2
The mass of an object never changes.

You might look into the kinetic energy of the branch. The faster it moves, the more energy it has, and the farther it falls, the faster it moves. It's easy to show that the energy of an object falling from height h and mass m has energy

[tex]E = (9.8\frac{\textrm{m}}{\textrm{s}^2})mh[/tex]

Edit: Just took out some superfluous information that might be a source of confusion.

cookiemonster
 
Last edited:
  • #3
[tex](9.8\frac{\textrm{m}}{\textrm{s}^2})mh = 1/2 mv^2[/tex]
Calculate v - velocity.


Hack, when I started, I’m going to finish it :) :
[tex] v ={\sqrt{2gh}}[/tex]
[tex]v= 4.43{\sqrt{h}}[/tex]
When you have h (height of that branch/three) you can calculate its velocity (you can see how it doesn’t depends on mass). But this is theoretical value calculated without air resistance (+ if the branch if alive with leafs, this “friction” factor is greater).

How much it weights? Weight is measure for force so you can calculate it (again theoretically) from:
[tex]F = m*a[/tex] you don’t know a, but let’s say that collision lasts t=0.3s, and branch decelerates form v to v=0, than you can say: [tex]a = v / t^2[/tex]. (you can use “ordinary” weight of branch as m).

Hope I helped,
Greetz

P.S. I have to mention that this is somehow interesting/funny to me, your fighting to cut tree, that as you say, endangers you, and we have an unexploded Tomahawk in our backyard, that we are too trying to get rid off :smile:. What a world :smile: (NHF – just comparing).
 

1. What is the formula for calculating the effective weight of a falling object?

The formula for calculating the effective weight of a falling object is W = mg - ma, where W is the effective weight, m is the mass of the object, g is the acceleration due to gravity, and a is the acceleration of the object.

2. How does air resistance affect the effective weight of a falling object?

Air resistance can decrease the effective weight of a falling object by counteracting the force of gravity. As the object falls, it experiences an upward force from the air resistance, which reduces the net force acting on the object and thus decreases its effective weight.

3. Does the shape or size of an object affect its effective weight when falling?

Yes, the shape and size of an object can affect its effective weight when falling. Objects with larger surface areas will experience more air resistance, which can decrease their effective weight. Additionally, objects with aerodynamic shapes may experience less air resistance and have a higher effective weight compared to objects with irregular shapes.

4. How does the altitude affect the effective weight of a falling object?

The altitude does not have a significant effect on the effective weight of a falling object. However, as the object falls from higher altitudes, it may experience a decrease in air density, which can affect the magnitude of air resistance and thus the effective weight.

5. Is the effective weight of a falling object the same as its actual weight?

No, the effective weight of a falling object is not the same as its actual weight. The actual weight of an object is the force of gravity acting on the object, while the effective weight takes into account other factors such as air resistance. The effective weight can be less than, equal to, or even greater than the actual weight depending on the circumstances.

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