ALGEBRA 2 WKST - Sault Schools
AP Worksheet 7.5 KEY
1. Find the work done by the force of [pic] Newtons along the x-axis from x = a meters to
x = b meters.
[pic]
2. The workers in Example 2 changed to a larger bucket that held 50L (490N) of water, but the new bucket had an even larger leak so that it too was empty by the time it reached the top. Assuming the water leaked out at a steady rate, how much work was done lifting the water this time? (Do not include the rope and bucket)
[pic]
3. The bucket in problem 2 is hauled up more quickly so that there is still 10L (98N) of water left when the bucket reaches the top. How much is work is done lifting the bucket this time? (Do not include the rope and bucket.)
[pic]
4. A spring has a natural length of 10 in. An 800-lb force stretches the spring to 14 in.
(a) Find the force constant.
(b) How much work is done in stretching the spring from 10 in. to 12 in.?
(c) How far beyond its natural length will a 1600-lb force stretch the spring?
[pic]
5. It takes a force of 21, 714 lb to compress a coil spring assembly on a New York City Transit Authority subway car from its free height of 8 in. to its fully compressed height of 5 in.
(a) What is the assembly’s force constant?
(b) How much work does it take to compress the assembly the first half inch? The second half inch? Answer the the nearest inch-pound.
[pic]
6. Suppose that gas in a circular cylinder of cross section area A is being compressed by a piston (see figure).
[pic]
(a) If p is the pressure of the gas in pounds per square inch and V is the volume in cubic inches, show that the work done in compressing the gas from state [pic]to state[pic]is given by the equation Work = [pic]in(lb, where the force against the piston is pA.
[pic]
(b) Find the work done in compressing the gas from [pic]to [pic]if [pic]and p and V obey the gas law [pic]= constant (for adiabatic processes).
[pic]
7. The rectangular tank shown here, with its top at ground level, is used to catch run off water. Assume that the water weighs [pic].
[pic]
(a) How much work does it take to empty the tank by pumping the water back to ground level once the tank is full?
[pic]
(b) If the water is pumped to ground level with a (5/11)-horsepower motor (work output 250 ft(lb/sec), how long will it take to empty the full tank (to the nearest minute)?
[pic]
(c) Show that the pump in part (b) will lower the water level 10 ft (halfway) during the first 25 min of pumping.
[pic]
8. A vertical right cylindrical tank measures 30ft high and 20 ft in diameter. It is full of kerosene weighing [pic].How much work does it take to pump the kerosene to the level of the top of the tank?
[pic]
9. Your town has decided to drill a well to increase its water supply. As the town engineer, you have determined that a water tower will be necessary to provided the pressure needed for distribution, and you have designed the system shown here. The water is to be pumped from a 300-ft well through a vertical 4-in pipe into the base of a cylindrical tank 20 ft in diameter and 25 ft high. The base of the tank will be 60 ft above the ground. The pump is a 3-hp pump, rated at 1650 ft[pic]lb/sec. To the nearest hour, how long will it take to fill the tank for the first time?
(Include the time it takes to fill the pipe.) Assume water weighs [pic].
[pic]
[pic]
10. A rectangular freshwater fish tank with base 2 x 4 ft and height 2ft (interior dimensions) is filled to within 2 in. of the top.
(a) Find the fluid force against each end of the tank.
[pic]
(b) Suppose the tank is sealed and stood on end (without spilling) so that one of the square ends is the base. What does that do to the fluid forces on the rectangular sides?
[pic]
11. A rectangular milk carton measures 3.75in. by 3.75in. at the base and is 7.75 in. tall. Find the force of the milk (weighing [pic]) on one side when the carton in full.
[pic]
11. A rectangular milk carton measures 3.75in. by 3.75in. at the base and is 7.75 in. tall. Find the force of the milk (weighing [pic]) on one side when the carton in full.
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