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Homework Statement
A spherical stone of mass 0.500 kg and radius 10 cm is launched vertically from ground level with an initial speed of 20.0 m/2. As it moves upwards, it experiences drag from the air as approximated by Stokes drag, F=6η∏Rv, where the viscosity of air is 1.002 mPa*s.
(a)Which forces are acting on the stone while it moves upward?
(b) Using Newton's second law of motion, write down an equation of motion for the stone this is a differential equation)
(c) Solve the differential equation to get an expression for v(t) for the stone.
(d) From (c) find the time at which the stone reaches its maximum height.
(e) From v(t), find h(t) for the stone (height as a function of time).
(f) Using (d) and (e), find the maximum height the stone reaches.
(h) Find the speed of the stone just before it hits the ground
Homework Equations
F=ma
a=dv/dt
The Attempt at a Solution
While the stone is moving upward, there is a gravitational force which is directed downwards. At the same time, there is a Stokes drag force directed downwards also(?).
(b). Newtons second law of motion: F=ma=m*(dv/dt). How should I continue.. Can anybody please help me with working out all these resting questions.. It would really help me with my understanding for such motions, and to develop some feeling for these problems.
Thank you in advance!