Math 241 Lots of practice - some we’ve done in class, most are new; mixed the types ofproblems, there are work with Hooke’s law, work with lifting cables , work with emptyingliquids, hydrostatic force (fluid force). A complete key will be posted soon.First a review of the units with workGiven the following table:System Force Distance WorkBritish Pounds(lbs) Feet(ft.) ft·lbInternational Newton Meter N· m=Joule(J)Notes about units;1. In the British system, the magnitude of the force = the weight, lbs, of the objectA pound =slug·ftsec22. In the International system, force = mass · acceleration,thus the force(N)=mass(kg) · 9.8msec2A Newton is akg·msec23. In the British system, the weight of water is given from 62.26lbsft3to 62.59lbsft3Pressure is measured inlbft24. In the International system, t h e weight of water is given by 9800Nm3=1000kgm39.8msec2Pressure is measured inNm2Assorted Problems1. A force of 9 lbs is requi r ed to str et ch a spring from its natural length of 6 inches to alength of 8 inches. Find t h e work done in stretching the spring(a) from its natural length to a length of 10 inches. (3ft-lbs)(b) from a length of 7 inches to a length of 9 inches. ( 1.5 ftl-lbs)2. A right circular conical tank has its axis vertical and its vertex at the bot t om . Theradius at the top is 10ft and the height of the tank is 30ft. It contains 12ft of water.Use the weight density of water as 62.4lbsft3. Find the work required to pump the wa te rout over the top. ( 263,472 ft-lbs)3. A5lbs hammer is lying at the b o t t o m of an empty well that is 16ft. deep. A ropeweighing116lbftis used to lift the hammer to the su r fa ce. How much work is done?(88 ft.-lbs)4. A tr o u g h having an isosceles t r a pezoidal cross section is full of water. If the trapezoidis 3ft wide at the top 2ft deep , find the to t a l force due to liquid pressure on one endof the trough. Use the water weight d en si ty of 62.4lbsft3(291.2 ft-lbs)5. It took 1800 Joules of work to stretch a spring from its natural length of 2m to a lengthof 5m. Find the spring’s force const a nt. (k=400Nm)6. A swi m m i n g pool is 20ft wide and 40ft. long and its bottom is an inclined plane, theshallow end having a depth of 3ft and the deep end,9ft. deep. If the pool is full ofwater, find the hydrostatic force on(a) the wall at the shallow end of the pool. (5616 lbs)(b) the wall at the deep end of the pool. (50625 lbs)(c) the wall along the side of the pool. (48672 lbs)7. A circular swimming pool has a di a m et er of 24 ft. the sides are 5ft deep and the depthof the water is 4ft deep. How much work is required to pump all the water out overthe side? The weight density of water is 62.4lbsft3. (338749 ft-lbs)8. An aquarium 2m long 1m wide and 1m deep is full of water. Find the work neededto p u m p hal f the water out of the aquarium. Use the density of water is 1000kgm3andgravity is 9.8ms2(2450 Joules)9. The ends of a trough are semicircles, each with a radius of 2ft. Find the hydrostaticfor on one of the trough if it is full of water. (332.8 lbs)10. Number 3 in the t ex t section page 43 - A spring is attached to a mass. It takes 50ft lbsof work to move it from x =1fttox =3ft. ataconstantspeed,whererestingpositionis x=0. What is the spring constant?