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musicfairy
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A small body of mass m located near the Earth’s surface falls from rest in the Earth's gravitational field. Acting on the body is a resistive force of magnitude kmv, where k is a constant and v is the speed of the body.
a) Write the differential equation that represents Newton's second law for this situation.
my answer: F = ma
a = dv/dt
F = mg - kmv
ma = mg - kmv
a = g - kv
dv/dt = g - kv
I'm pretty sure I got this one right.
b) Determine the terminal speed vT of the body.
F = 0
g - kv = 0
g = kv
vT = g / k
I think I got this one right too.
c) Integrate the differential equation once to obtain an expression for the speed v as a function of time t. Use the condition that v = 0 when t= 0.
What I did so far:
dv/dt = g - kv
dt = dv / (g - kv)
So I would integrate dt = dv / (g - kv). The problem is I don't know how. Can someone please explain how to do this kind of integration, why I would do it that way?
a) Write the differential equation that represents Newton's second law for this situation.
my answer: F = ma
a = dv/dt
F = mg - kmv
ma = mg - kmv
a = g - kv
dv/dt = g - kv
I'm pretty sure I got this one right.
b) Determine the terminal speed vT of the body.
F = 0
g - kv = 0
g = kv
vT = g / k
I think I got this one right too.
c) Integrate the differential equation once to obtain an expression for the speed v as a function of time t. Use the condition that v = 0 when t= 0.
What I did so far:
dv/dt = g - kv
dt = dv / (g - kv)
So I would integrate dt = dv / (g - kv). The problem is I don't know how. Can someone please explain how to do this kind of integration, why I would do it that way?