Force exerted to a falling object

In summary, using the law of conservation of energy, the velocity of the rock just before collision was found to be 6.3 m/s. The velocity becomes 0 due to resistance force, which leads to an acceleration of 330.75 m/s^2. Multiplying this by the mass of the rock (120 N/9.8 m/s^2), the Earth's average force of resistance is calculated to be approximately 4.1 kN.
  • #1
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Homework Statement



A rock with a weight of 120 N free falls from height of 2.00m collides with with Earth and digs 60 mm into it. What is the Earth's average force of resistance

Homework Equations



F=m*g => m=F/g

m*g*h = 1/2*m*v^2

v=√(2*g*h)

The Attempt at a Solution



I found the velocity of a rock just before collision using the law of conservation of energy. I now know the velocity which I got 6.3 m/s but now I am stumped on how do i find the forces exerted by Earth to stop the rock from digging deeper.
 
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  • #2
Hmm i would do it another way

Before hitting ground its velocity is 6.3m/s right??

So that velocity becomes 0 due to some acceleration (due to resistance force)

so using v2-v02=2(a)(s)

u find acceleration (retardation in this case)

now that multiplied to the mass will give u the force...

Hope it helps
 
  • #3
Think of the 20mm as a 'stopping distance'.
 
  • #4
i assume you substitute s with 0.006 m right. I tried that in that case

[itex]v^{2}_{f}[/itex]=[itex]v^{2}_{i}[/itex] + 2 * a * x

0=6.3^{2}+2*a*0.06
0=39.69+0.12a
-0.012a=39.69 / (-0.12a)
a=330.75 m/s^2

F=m*a

F= 12 * 330.75 = 3969 N

however the answer should be 4.1 kN
 
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  • #5
use mass = 120/9.8

it gives an approximate answer
 
  • #6
getting closer :P thanks I guess it was just an error in rounding the number
 

What is the force exerted on a falling object?

The force exerted on a falling object is called the weight. It is equal to the mass of the object multiplied by the acceleration due to gravity.

How does the force exerted on a falling object change during its fall?

The force exerted on a falling object remains constant throughout its fall. This is because the acceleration due to gravity, which determines the weight, remains constant near the Earth's surface.

What factors affect the force exerted on a falling object?

The force exerted on a falling object is affected by its mass and the strength of the gravitational field it is falling in. Air resistance may also play a role in the force exerted on the object.

Does the shape of a falling object affect the force exerted on it?

The shape of a falling object may affect the force exerted on it due to air resistance. Objects with a larger surface area will experience more air resistance and therefore may experience a different force than objects with a smaller surface area.

What is the relationship between force exerted and the speed of a falling object?

The force exerted on a falling object is directly proportional to its acceleration, which is also directly proportional to its speed. This means that as the speed of a falling object increases, so does the force exerted on it.

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