1.)A cable hangs between two poles of equal height

and 20 feet apart. Set up a coordinate system where the poles are placed at x =

-10 and x = 10, where x is measured in feet. The height (in feet) of the cable

at position x is h(x) = 12 \cosh(x/12),where \cosh(x) = (e^x + e^{-x})/2 is

the hyperbolic cosine.

How long is the cable in feet?

2.)A bucket of water of mass 20 kg is pulled at constant velocity up to a platform 40 meters

above the ground. This takes 16 minutes, during which time 7 kg of water drips

out at a steady rate through a hole in the bottom. Find the work needed to raise

the bucket to the platform. (Use g = 9.8 {m/s}^2.)

3.)A gas station stores its gasoline in a tank under the ground. The tank is a cylinder lying

horizontally on its side. (In other words, the tank is not standing vertically

on one of its flat ends.) If the radius of the cylinder is 0.5 meters, its

length is 2 meters, and its top is 1 meter under the ground, find the total

amount of work needed to pump the gasoline out of the tank. (The density of

gasoline is 673 kilograms per cubic meter; use g=9.8{ m/s}^2.)

4.)A large tank is designed with ends in the shape of the region between the curves

y=x^2/2 and y=10, measured in feet. Find the hydrostatic force (in lb) on one

end of the tank if it is filled to a depth of 8 ft with gasoline. Assume the

gasoline's weight density is 42.0 lb/ft^3. (In British units, "weight density"

is the equivalent of g in SI units.)

5.)Calculate the fluid force on the shaded side of the triangular plate submerged in fluid with mass density =

850{kg/m}^3 shown in the figure. (Length is in meters. Note also that the base

triangle shown in the figure is parallel to the surface of the fluid, and the

angle 60 degree is the angle between the shaded triangle and based triangle.)