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4. 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 2kg falling underwater vertically faces a retarding force of magnitude 10kg/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 = 20N (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) = -5ms-¹.

4. 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 2kg falling underwater vertically faces a retarding force of magnitude 10kg/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 = 20N (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) = -5ms-¹.

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4. 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 2kg falling underwater vertically faces a retarding force of magnitude 10kg/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 = 20N (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) = -5ms-.
Transcribed Image Text:4. 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 2kg falling underwater vertically faces a retarding force of magnitude 10kg/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 = 20N (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) = -5ms-.
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