Finding Acceleration of Falling Object: Newton's 2nd Law

In summary, the conversation discusses the use of Newton's 2nd law of motion to find the acceleration of a body falling vertically under gravity in a medium with resistive force proportional to the speed of the body. The resulting equation is m = g(1-(v/vt)n), where n is a positive constant and vt is the terminal velocity of the body. The conversation also explores different possibilities for the equation, including the addition of a constant and the use of a constant multiplier.
  • #1
LukeEvans
22
0
A body of mass m (kg) is falling vertically under gravity g m/s2 in a medium whose resistance to the speed of the body, v m/s, is proportional to vn (n positive).

If the body was released from rest and has terminal velocity, vt m/s, use Newton's 2nd law of motion to show that its acceleration, a m/s2, may be expressed as

a = g(1-(v/vt)n)

(4 Marks)


I would obviously like to attempt to solve this problem, but am unsure what the first step should be. Perhaps the resistive force will need to be deducted from the velocity... many thanks to anybody who looks.
 
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  • #2
Hi LUke! :smile:

start by writing the first sentence as an equation …
LukeEvans said:
A body of mass m (kg) is falling vertically under gravity g m/s2 in a medium whose resistance to the speed of the body, v m/s, is proportional to vn (n positive).
 
  • #3
A body of mass m (kg) is falling vertically under gravity g m/s2 in a medium whose resistance to the speed of the body, v m/s, is proportional to vn (n positive).

m = g - vn

would be an uneducated guess :tongue:
 
  • #4
what about "proportional to" ?
 
  • #5
m = g - (v*vn)

possibly?
 
  • #6
LukeEvans said:
m = g - (v*vn)

possibly?

That's g - vn+1

how is vn+1 proportional to vn ? :confused:
 
  • #7
how about:

m = g * vn

or

m = g*(v+vn)
 
  • #8
:rolleyes:

Suppose I told you that the medium's resistance was 3vn, what would the equation be then?
 
  • #9
m = g - 3vn

I'll be honest I don't know where the 3 has come from.
 
  • #10
the resistive force is proportional to vn.

3 is proportional

it has to be something
 
  • #11
Right.

m = g - vvn
 
  • #12
How does that look?
 
  • #13
" proportional to vn " means kvn for some constant k
 

1. What is Newton's 2nd Law?

Newton's 2nd Law is a fundamental law of physics that states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass.

2. How do you find the acceleration of a falling object using Newton's 2nd Law?

To find the acceleration of a falling object using Newton's 2nd Law, you need to know the net force acting on the object and its mass. Then, you can use the formula a = F/m to calculate the acceleration.

3. What is the relationship between force and acceleration according to Newton's 2nd Law?

According to Newton's 2nd Law, force and acceleration are directly proportional. This means that as the force acting on an object increases, its acceleration also increases.

4. How does the mass of an object affect its acceleration?

The mass of an object has an inverse relationship with its acceleration according to Newton's 2nd Law. This means that as the mass of an object increases, its acceleration decreases.

5. Can Newton's 2nd Law be used to find the acceleration of any object?

Yes, Newton's 2nd Law can be used to find the acceleration of any object as long as the net force acting on the object and its mass are known. This law applies to all objects, regardless of their size or shape.

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