Calculating Velocity: Force, Mass & Distance Relationship

AI Thread Summary
The discussion centers on calculating the velocity of a 1kg mass influenced by a force inversely proportional to the square of the distance from a point. The force equation is given as f = 10000/(y^2), leading to the acceleration a = 10000/(y^2). To find the velocity as a function of time, it is suggested to first derive the velocity in terms of the distance y, as y changes as the body moves closer to the point. Utilizing energy conservation principles is recommended to simplify the calculations. The main goal is to establish a clear velocity equation for the body attracted to another point.
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I have a body of 1kg of mass being acted on by a force of magnitude equal (10000/(y^2))
[where y is the distance between the body and a certain point] and this force is in the direction pointing to the point
so depending on what mentioned above :-
what i know is : f = a = (1000 0/(y^2))
and that Dy/Dt = V (velocity)

What is needed is the function of the velocity in terms of time.
Thanks for reading.
 
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As you have said a=10000/(y^2)
==>Dv/Dt=10000/(y^2)
if y is a fixed value and independent of time ,integrating with respect to t

v=10^5(t)
-------
y^2
 
ofcourse y is not a constant value since the distance which is y decreases as the body moves towards the point
 
any help ??
 
is it this hard i just want to know the velocity equation between body attracted to a point or another body!
 
You probably need to find the velocity as a function of distance y first. Using energy conservation would help with that.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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