Work: springs, pumping and cables practice problems
Work as force times distance, added up: springs, pumping water out of a tank, winding up a cable. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
A cylindrical tank of radius 2 m and height 2 m holds water to a depth of 2 m. How much work does it take to pump all the water out over the top? (Water weighs \( \displaystyle 9800\ \text{N/m}^3 \).)
A force of 30 N holds a spring stretched \frac{1}{5} m beyond its natural length. How much work does it take to stretch it from \frac{2}{5} m to \frac{1}{2} m beyond its natural length?
A 30-ft cable weighing 3 lb/ft hangs from the top of a building with a 25-lb load on its end. How much work does it take to pull it all to the top?
A cylindrical tank of radius 4 m and height 3 m holds water to a depth of 3 m. How much work does it take to pump all the water out over the top? (Water weighs \( \displaystyle 9800\ \text{N/m}^3 \).)
A force of 30 N holds a spring stretched \frac{1}{5} m beyond its natural length. How much work does it take to stretch it from 0 m to \frac{1}{5} m beyond its natural length?
A cylindrical tank of radius 2 m and height 3 m holds water to a depth of 1 m. How much work does it take to pump all the water out over the top? (Water weighs \( \displaystyle 9800\ \text{N/m}^3 \).)
A force of 30 N holds a spring stretched \frac{1}{4} m beyond its natural length. How much work does it take to stretch it from \frac{1}{5} m to \frac{2}{5} m beyond its natural length?
A 40-ft cable weighing 1 lb/ft hangs from the top of a building. How much work does it take to pull it all to the top?
A cylindrical tank of radius 1 m and height 5 m holds water to a depth of 1 m. How much work does it take to pump all the water out through a spout 1 m above the top? (Water weighs \( \displaystyle 9800\ \text{N/m}^3 \).)
A force of 12 N holds a spring stretched \frac{1}{10} m beyond its natural length. How much work does it take to stretch it from \frac{3}{10} m to \frac{2}{5} m beyond its natural length?