Avon High School
AP Calculus BC
Name ______________________________________
Period _____
Score ______ / 10
HW 7.5 B – Supplementary Work Problems
1.) A mountain climber is about to haul a 50 meter length of hanging rope. How much work will it take if
each meter of rope weighs 0.74 lbs.
2.) A model rocket engine burned up its 3-oz. fuel cartridge lifting the rocket to 180 ft. Assuming that the fuel
burned at a steady rate, how much work was spent lifting the fuel alone?
3.) An electric elevator with a motor at the top has a multi-strand cable weighing 5 lb/ft. 200 feet of cable are
paid out when the car is at the first floor and effectively zero feet are out when the car is at the top floor.
How much work does the motor do just lifting the cable when it takes the car from the first floor to the top
floor?
4.) A bag of sand that originally weighed 144 lb was lifted at a constant rate. The sand leaked out at a steady
rate and the sand was half gone by the time the sandbag had been lifted 12 ft. How much work was done in
lifting the sand this far? (Neglect the bag’s weight and the weight of the lifting equipment.)
5.) If a force of 6 Newtons stretches a spring 0.4 meters beyond its natural length, how much work is done?
6.) If a force of 90 Newtons stretches a spring 1 meter beyond its natural length, how much work does it take to
stretch the spring 5 meters beyond its natural length?
7.) A 10,000-lb force compressed a spring from its natural length of 12 inches to a length of 11 in. How much
work did it do in:
a) compressing the spring the first half inch?
b) compressing the spring the second half inch?
8.) A vertical right cylindrical tank measures 28 ft high and 20 ft in diameter. It is full of kerosene weighing
51.2 m/ft3. How much work does it take to pump the kerosene to the level of the top of the tank?
9.) The rectangular tank shown here with its top at ground
level is used to catch runoff water. Water density is
62.5 lb/ft3.
a) How much work does it take to empty the tank once the
tank is full?
b) If the water is pumped to ground level with a
5
-hp motor (work output 250 ft-lb/sec), how long will it
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take to empty the tank.
c) Show that the pump in part (b) will lower the water level to 10 ft (halfway) within the first half hour.
10.) The full rectangular cistern (rainwater storage tank) shown
here with its top 15 ft below ground level is to
be emptied for inspection by pumping its contents to ground
level.
a) How much work will it take to empty the cistern?
b) How long will it take a
3
-hp pump (rated at 300 ft-lb/sec to pump the tank dry?
4
c) How long will it take the pump in part (b) to empty the tank halfway?
11.) You are in charge of the evacuation and repair of the storage tank shown in the following diagram. The
tank is a hemisphere of radius 12 ft and is full of benzene weighing 56 lb/ft3. A firm you contacted says it
can empty the tank for 0.25 cents per foot-pound of work. Find the work required to empty the tank by
pumping the benzene to an oulet 2 ft above the top of the tank. If you have $5,000 budgeted for the job,
can you afford to hire the firm?
1
oz/in3. As you can see, the
2
container is 7 in. deep, 2.5 in across the base, and 3.5 in across the top (a standard-sized milkshake). The
straw sticks up an inch above the top of the container. About how much work does it take to suck up the
milkshake through the straw (ignoring friction).
12.) The truncated container below is full of strawberry milkshake that weighs