Physics

Problem

A small tower is built by placing three identical wooden blocks one above the other on level ground. Each block has mass

2\,\text{kg}

and thickness

8\,\text{cm}

. a. (i) Draw a labelled sketch showing the positions of the centres of mass of the three blocks after the tower is built. b. (ii) Taking the ground as the reference level for potential energy and

g = 10\,\text{m s}^{-2}

, calculate the gravitational potential energy possessed by each block in the tower. c. (iii) Hence determine the total gravitational potential energy stored in the tower. d. (iv) The blocks are now dismantled one by one and each block is placed on a table

1.0\,\text{m}

high. Calculate the additional energy required to place all three blocks on the table.

Intuitive explanation

The key here is understanding center of mass and stability. For the tower not to topple, the combined center of mass of all blocks above any given level must stay directly over the base of support. Start by finding where the center of mass of the top blocks sits relative to the block below, then work downward to see how much horizontal overhang each level can safely have before tipping.

Intuitive explanation

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