5. A ball of mass m gm and radius 7 cm is released from rest in a liquid of viscosity gm/(cm sec). The ball falls under the influence of gravity but the liquid exerts a drag proportional to its velocity v cm/sec. If y cm measures the vertical distance the ball has fallen, then its equation of motion is m d²y dt² dy + 6πμη = mg. dt Determine y(t). What can you say about the velocity v(t)? Suppose a steel ball of density p = 8 gm/cc is dropped in water (μ = 0.01 gm/(cm sec)). Determine the radius of the ball that will fall steadily at 5.05 mph (the fastest speed of a swimmer). Answer: 0.35 mm.

what is the equilibrium of dy/dx = y - sqrt(y) when y >0

A 100-W (watt) light bulb has resistance R = 143 2 (ohms) when attached to household current, where voltage varies as V = Vo sin(27ft), where Vo = 110 V, f = 60 Hz. The power supplied to the bulb is P = J/s (joules per second) and the R total energy expended over a time period [0, T] (in seconds) is T U = P(t) dt Compute U if the bulb remains on for 7 hours. (Use decimal notation. Give your answer to one decimal place.) U = J

Answer all parts