ok here's what I did
integrated F with respect to r and got W
W=-k/r + c1
using W = -\DeltaU I found U to be k/r
I then used the expression
\textbf{E} = \frac{k}{r1} +\frac{1}{2}mv1^{2} = \frac{k}{r2} +\frac{1}{2}mv2^{2}
and since v1= 0 and r1=0
\textbf{E} = \frac{k}{r1} =...
K is given as a constant, analogous to Coulombs or the gravitational constant. The force could be expressed as
F = -k/r^2 = m\ddot{x}
and we can see that acceleration is as always inversely proportional to the mass of the particle.
I believe you need to use U to solve this problem but...
Homework Statement
a particle of mass m is attracted to the origin by a force F=-k/r^2
find the time t for the mass to reach the origin
Homework Equations
\DeltaU= U-U0 = \int\textbf{F}(r) dr
The Attempt at a Solution
I found \DeltaU by \DeltaU= U-U0 = \intF(r) dr and by...
hey thanks a lot both of you guys!
hate to keep pestering but if I want to find x(t) I just integrate dx/dt and find a new constant C3 using the initial condition x(0) t=0?
v_0=v(t=0)
(e^20\alpha)/\alpha = C3
C3 = 73.8
v(t) = (ln(-At\alpha)+ ln(73.8\alpha))/alpha
sorry if I am a little slow with this, am I making an error here?
thanks for responding gabba,
I think that I tried the separable differential equations method but couldn't make sense of the answer
what i did was
e^(\alphav) dv = -Adt
1/\alpha(e^(\alphav)-e^(\alphav0)) = -At
i'm not sure what this means though or where to go from here
Homework Statement
Given the one-dimensional retarding force F=-Ae^(-\alphav) find an expression for v(t).
Homework Equations
F = m(dV/dt)
A and \alpha are constants, v is instantaneous speed.
The Attempt at a Solution
Im not sure how to frame the idea of integrating a...