Lifting Books - Potential Energy

AI Thread Summary
To determine the minimum work required to stack six books, each weighing 30N and 4cm thick, the student needs to calculate the potential energy involved in lifting each book to its respective height. The mass of each book is approximately 3.06kg, and the relevant equation for potential energy is Ep = mgh, where h increases with each book added to the stack. The total height for each book must be considered, as the first book requires no lift, the second book is lifted 0.04m, and so on, leading to a cumulative height for each subsequent book. The minimum work is achieved by moving the books at a constant speed, which simplifies the calculations. Understanding the relationship between work, mass, gravity, and height is crucial for solving this problem effectively.
Ipos Manger
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Homework Statement


A student has six books, all of them with a 4cm thickness and a weight of 30N. ¿What would be the minimum work to put the books in one pile, if the six books are in a table?

Weight: 30N
Thickness: 4cm.
Gravity: 9.81ms-2

Homework Equations



Ep=mgh

Ec=(mv2)/2

The Attempt at a Solution



I found the mass of each book, which is 3.06kg, and converted the thickness to m, 0.04m.

After that, I'm lost. :S I don't know how to work it out..
 
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You need to find the amount of work it takes to put one book on top of another book! You know that the work needed to move one book onto the other one is:

(the mass of the book) * (the acceleration due to gravity) * (the height the book must be lifted).

Think about what the height will be that you must lift each book (HINT: it's a number that will increase for each book you stack onto your stack!)
 
Ipos Manger said:

Homework Statement


A student has six books, all of them with a 4cm thickness and a weight of 30N. ¿What would be the minimum work to put the books in one pile, if the six books are in a table?

Weight: 30N
Thickness: 4cm.
Gravity: 9.81ms-2

Homework Equations



Ep=mgh

Ec=(mv2)/2

The Attempt at a Solution



I found the mass of each book, which is 3.06kg, and converted the thickness to m, 0.04m.

After that, I'm lost. :S I don't know how to work it out..
Your relevant equations talk about potential and kinetic energy, but I think you are looking for the minimum work done by the student (not the total work done, although the problem is not worded clearly that way). Minimum work ocurs when the books are moved slowly at constant speed. What equations do you know for work done at constant speed?
 
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