(a) A ball of mass 5kg falling underwater vertically faces a retarding force of magnitude 15kg/s times its magnitude of velocity (lets call the velocity v; note the retarding force is proportional to the velocity). The ball also experiences a downward force of mg = 50N (taking g = 10ms-2 for this problem). Taking the upward direction as positive (note this means v < 0 as the ball moves down), write down the resultant force acting on the ball. (b) Now equate ma with your result from a) (using Newton's law) and solve the first order ODE in terms of v (remember that a = dv/dt) with the initial condition that v(0) = -10ms-. (c) We can find the displacement of the ball in the same manner (as a = dx/dt? and v = dx/dt) and proceed to solve the 2nd order ODE. How- ever, we can simply integrate the velocity to obtain the displacement. Use either method you prefer to obtain the displacement with the initial condition r(0) = -3m.
(a) A ball of mass 5kg falling underwater vertically faces a retarding force of magnitude 15kg/s times its magnitude of velocity (lets call the velocity v; note the retarding force is proportional to the velocity). The ball also experiences a downward force of mg = 50N (taking g = 10ms-2 for this problem). Taking the upward direction as positive (note this means v < 0 as the ball moves down), write down the resultant force acting on the ball. (b) Now equate ma with your result from a) (using Newton's law) and solve the first order ODE in terms of v (remember that a = dv/dt) with the initial condition that v(0) = -10ms-. (c) We can find the displacement of the ball in the same manner (as a = dx/dt? and v = dx/dt) and proceed to solve the 2nd order ODE. How- ever, we can simply integrate the velocity to obtain the displacement. Use either method you prefer to obtain the displacement with the initial condition r(0) = -3m.
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Recall that Newton’s law is F = ma, where F is the net force, m is the mass
and a is the acceleration of the object. At first this may not look like it, but
this is actually a differential equation.
Transcribed Image Text:(a) A ball of mass 5kg falling underwater vertically faces a retarding force of
magnitude 15kg/s times its magnitude of velocity (lets call the velocity
v; note the retarding force is proportional to the velocity). The ball also
experiences a downward force of mg = 50N (taking g = 10ms-2 for this
problem). Taking the upward direction as positive (note this means v < 0
as the ball moves down), write down the resultant force acting on the
ball.
(b) Now equate ma with your result from a) (using Newton's law) and solve
the first order ODE in terms of v (remember that a = dv/dt) with the
initial condition that v(0) = –10ms-1.
(c) We can find the displacement of the ball in the same manner (as a =
dx/dt2 and v = dx/dt) and proceed to solve the 2nd order ODE. How-
ever, we can simply integrate the velocity to obtain the displacement.
Use either method you prefer to obtain the displacement with the initial
condition r(0) = -3m.
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