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. (a) A ball of mass 7kg falling underwater vertically faces a retarding force of magnitude 14kg/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 (where m is the mass and g = 10ms-2). 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 = initial condition that v(0) = -4ms-1. dv/dt) with the (c) We can find the displacement of the ball in the same manner (as a = dx/dt? and v = ever, we can simply integrate the velocity to obtain the displacement. Use either method you prefer to obtain the displacement with the initial condition x(0) = -2m. dx/dt) and proceed to solve the 2nd order ODE. How-
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. (a) A ball of mass 7kg falling underwater vertically faces a retarding force of magnitude 14kg/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 (where m is the mass and g = 10ms-2). 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 = initial condition that v(0) = -4ms-1. dv/dt) with the (c) We can find the displacement of the ball in the same manner (as a = dx/dt? and v = ever, we can simply integrate the velocity to obtain the displacement. Use either method you prefer to obtain the displacement with the initial condition x(0) = -2m. dx/dt) and proceed to solve the 2nd order ODE. How-
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Transcribed Image Text:5. 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.
(a) A ball of mass 7kg falling underwater vertically faces a retarding force of
magnitude 14kg/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 (where m is the mass and g
10ms-2). 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 =
initial condition that v(0) = -4ms¬1.
dv/dt) with the
(c) We can find the displacement of the ball in the same manner (as a =
dx/dt? and v =
ever, we can simply integrate the velocity to obtain the displacement.
Use either method you prefer to obtain the displacement with the initial
condition x(0) = -2m.
dx/dt) and proceed to solve the 2nd order ODE. How-
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