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[SOLVED] Mechanics question - help please?
Hey, I've just signed up here, and not entirely sure if I'm posting in the right place. But I have a Mechanics question, which has confused me, so here goes:
A bead of mass m is threaded onto a horizontal wire. When moving with speed u, the retarding force of air resistance is known to be ku^2 where k is a constant. Write down an equation of motion for the bead that describes the speed u in terms of the time t, and hence show that:
(m/u) = (m/u0) + kt
if u = u0 when t = 0.
I guess F = ma ?
Since the retarding force is given by ku^2 I tried letting a = (F/m) = (-ku^2)/m and then writing that u = u0 - (ktu^2)/m, because the speed should be the initial speed plus (acceleration x time) right? But when I re-arrange this equation to get something in terms of (m/u) it doesn't give me the right answer. Am I even on the right lines?
Hey, I've just signed up here, and not entirely sure if I'm posting in the right place. But I have a Mechanics question, which has confused me, so here goes:
Homework Statement
A bead of mass m is threaded onto a horizontal wire. When moving with speed u, the retarding force of air resistance is known to be ku^2 where k is a constant. Write down an equation of motion for the bead that describes the speed u in terms of the time t, and hence show that:
(m/u) = (m/u0) + kt
if u = u0 when t = 0.
Homework Equations
I guess F = ma ?
The Attempt at a Solution
Since the retarding force is given by ku^2 I tried letting a = (F/m) = (-ku^2)/m and then writing that u = u0 - (ktu^2)/m, because the speed should be the initial speed plus (acceleration x time) right? But when I re-arrange this equation to get something in terms of (m/u) it doesn't give me the right answer. Am I even on the right lines?