Thread: Need help with 4 word problems dealing with Work force and Moment

Can anyone help me with any of these 4 problems?

1/ It requires 60 in-lb of work to stretch a certain spring from a length of 6 inches to 7 inches and another 120 in-lb of work to stretch it from 7 inches to 8 inches. Find the spring constant and the natural length of the spring.

2/ A plate having the shape of an isosceles trapezoid with upper base 4 feet long and lower base 8 feet long is submerged vertical in water such that the bases are parallel to the surface. If the distances from the surface of the water to the lower and upper bases are 10 feet and 6 feet, respectively, find the force exerted by the water on one side of the plate.

3/ Find the center of mass of a thin plate of constant density covering the given region bounded by the curves .

4/ A right circular conical tank of altitude 20 feet and radius of base 5 feet has its vertex at ground level and axis vertical. If the tank is full of water weighing 62.5 lb/ft3, find the work done in pumping all the water thru a pipe that rises to a height of 2 feet above the top of the tank.

work problems ...

1. let = spring's natural length in inches ...





you should be able to get two equations in terms of and from the definite integrals


4. work =

= weight density = 62.5

= cross-sectional area of a horizontal slice of water in terms of y ,

= lift distance of a cross-sectional slice in terms of y ,

= slice thickness =

i got the last 3.. still need help with the first. how do i get the equations?

edit: thanks, i have completed the problems.