Science:Math Exam Resources/Courses/MATH101/April 2015/Question 09 (b)/Solution 1

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First, calculate the work required to move the iron plate at the height with the width .

Since we move from the 2m basement below ground level, the distance that the object move is .

On the other hand, since the plate at the height is a square with the side length , its volume is .

Using the formula for the mass, this gives the mass of the plate: .

Then, from the formula for the force, we have .

Therefore, the required work to move the iron plate at the height is

Finally, since the range of is from to , we integrate in this range and get the total required work to move all of the iron from its starting position to its present position: