Calculate Force F of Falling Object with Mass m and Velocity v

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In summary: FT=change in momentum Ft=change in mass v=initial velocity u=final velocity v^{2}=initial velocity multiplied by 2
  • #1
KingNothing
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If an object of mass m is falling, and hits the ground at velocity v, and makes an indent in the ground of length d, what is the force F that he hits with?

I'm just asking what equations you would use.
 
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  • #2
Sounds like a momentum question...

Ft=change in mv.
You have mv change, and are asked for F, so you need t. Calculate this from s=d/t


... and post questions like this in the HWK section!
 
  • #3
How do you know how long the interaction with the ground was (dt)?
 
  • #4
Originally posted by Adrian Baker
Sounds like a momentum question...

Ft=change in mv.
You have mv change, and are asked for F, so you need t. Calculate this from s=d/t


... and post questions like this in the HWK section!

This is not quite right. s=d/t is only valid for constant velocity motion. You certainly do not have that here.

There are typically three simple kinematics equations that I tell most students to remember, or be able to derive. Most intro physics courses use these, and they are (under the assumption of constant acceleration a):

[tex] s=s_{0} + ut+ 1/2 at^{2}[/tex]

[tex] v=u + at[/tex]

[tex] v^{2} = u^{2} + 2as[/tex]

where s=displacement at time t, u is the initial velocity, and v is the velocity at time t. Note that these are NOT three separate equations. They are the same thing, only expressed in different "forms", which means that they are derivable from each other.

Now there are several ways to do this problem. Since F=ma is obvious, if we can find "a" during the relevant part of this problem, we are done. The 3rd equation I listed above has all the necessary ingredients necessary to find the acceleration if you assume that the deceleration is a constant, since you know the distance travelled, s (=d), you know v (i.e. zero), you know u (equivalent to the "v" in the problem -- I know, this can be confusing).

Zz.
 
  • #5
I do not see how you can get any meaningful answer without some knowledge of the "ground". The same ball falling at the same speed will make a way different dent in sand then granite. The concept of the dent implies that the material did some work stopping the falling body, this work is the force times the distance in this case the distance will be the depth of the dent, the force will be either the change in momentum or mass times acceleration, for either of those we need to know the time required to stop the falling body, this would come from knowing the properties of the material.
 
  • #6


Originally posted by Decker
If an object of mass m is falling, and hits the ground at velocity v, and makes an indent in the ground of length d, what is the force F that he hits with?

I'm just asking what equations you would use.

I would use the same equation I posted for your other question.

[tex]F_{ground} = \frac{\frac{1}{2}mv^2 + mgd}{d}[/tex]


g is gravity.
 
  • #7
apply v(square) - u(square)=2as

u=v is the initial as it stops after penetrating ...v=0


u can calculate "a" from here

then F=ma is the resistance provided by the ground when it is penetrating in the ground...

And the force with which it hits the ground = ma

find the "a" from kinematics equations
 

1. How do you calculate the force of a falling object?

The force of a falling object can be calculated using the formula F = m x a, where m is the mass of the object and a is the acceleration due to gravity (9.8 m/s^2). This means that the force (F) is equal to the mass (m) of the object multiplied by the acceleration (a) it experiences as it falls.

2. What is the formula for calculating force?

The formula for calculating force is F = m x a, where F is the force, m is the mass of the object, and a is the acceleration. This formula is also known as Newton's Second Law of Motion.

3. How does the mass and velocity of an object affect the force when it falls?

The force of a falling object is directly proportional to its mass and velocity. This means that the greater the mass and velocity of the object, the greater the force it will experience as it falls.

4. Can the force of a falling object be negative?

No, the force of a falling object cannot be negative. Force is a vector quantity, meaning it has both magnitude and direction. When an object falls, the force acting on it is always directed towards the center of the Earth, so it cannot be negative.

5. Is air resistance a factor in calculating the force of a falling object?

Yes, air resistance can affect the force of a falling object. Air resistance is a force that opposes the motion of an object through the air. As an object falls, it experiences air resistance, which can reduce its velocity and therefore the force it experiences. However, for most practical purposes, the effect of air resistance is negligible and can be ignored in the calculation of force for falling objects.

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