I agree with this and see were it comes from
net force = (delta p)/t
so momentum is conserved when net force equals zero...
net force = (delta p)/t
0 = (delta p)/t
however the following is not true
0 = (delta p)/t = P - Po
were p is momentum and Po is used to indicate inital and P final
can you please help me prove that when no net forces act on an object momentum is conserved... because I don't see how the t in the equaion just gets to magically dissapear... I was think along the lines of you can't divide by zero therefore delta p must be equal to zero which lead me to get
P = Po
but then I rembered that I was actually doing math and that you can divide by zero
so I don't get it please show me how the t just magicall dissapears
I agree with this
(P - Po)/t = 0
P/t - Po/t = 0
P/t = Po/t
how come i can just take the t out
but don't see were this comes from
The more correct way to write the change of momentum equation is
F = (delta p)/(delta t)
If there is a time-varying force, the above equation applies for short time intervals, in the limit as delta t approaches zero. Using calculus notation, one writes
f = dp/dt
If there is NO force, p never changes, regardless of the time interval.
To understand why the time component (t) "disappears" when no net forces act on an object, let's break down the equation and concept of momentum conservation.
First, let's start with the definition of momentum:
Momentum (p) = mass (m) x velocity (v)
The change in momentum (Δp) is the difference between the final momentum (P) and the initial momentum (Po):
Δp = P - Po
Now, let's consider Newton's second law of motion:
Force (F) = rate of change of momentum (Δp) / time (t)
Using the equation for force, we can rewrite it as:
F = (P - Po) / t
If there is no net force acting on an object (F = 0), we have:
0 = (P - Po) / t
To solve for momentum conservation, we need to isolate Δp by multiplying both sides of the equation by t:
0 = (P - Po)
So, when no net forces act on an object, the change in momentum (Δp) is equal to zero.
To answer your question about the "magical disappearance" of time (t), it's important to understand that the equation represents the condition of momentum conservation. When there are no net forces acting on the object, the change in momentum (Δp) and time (t) both become irrelevant because there is no acceleration or change in velocity. In other words, the object's momentum remains constant (P = Po) over time. This concept is supported by Newton's first law of motion, which states that an object at rest will remain at rest, and an object in motion will continue moving with a constant velocity, unless acted upon by an external force.
So, when analyzing momentum conservation in the absence of net forces, we can simplify the equation to:
P = Po
This equation reflects the fact that momentum is conserved when there are no net forces acting on an object.