What does this value represent in this work question?

[AJKing]

Answered this myself as I wrote it.

Homework Statement

Eight bricks, each 6.0 cm thick with a mass of 1.5 kg, lie flat on a table. How much work is required to stack them one on top of another?

h_brick = 0.060 m
m = 1.5 kg

Homework Equations

W = Fd
F_g = m*g

The Attempt at a Solution

I tried the following, and was correct. Please read the fourth point for my question.

F_g = 1.5*9.8 = 14.7 N

W_t = W₁+W₂+W₃+W₄+W₅+W₆+W₇+W₈

W_t = 14.7*0 + 14.7*.06 + . . . + 14.7*0.42 = 25 J4. My question

The answer to the question goes a little something exactly like this:

8 bricks each with m = 1.5 kg
height of each brick h= 0.060m
centre of mass is lifted 3.5 h

W = (8*1.5*9.8)(3.5*0.060) = 25 J

Where did that 3.5 come from?

7 bricks lifted divided by 2? Oh . . . Probably. Yeah. Averages and what not.

Writing this helped. Might as well post it.

 

[CompuChip]

Yep. Your calculation is
$$W_t = 1.5 \times 9.81 \times (0.06 \times 0 + 0.06 \times 1 + \cdots + 0.06 \times 7)$$
Since (1 + 2 + ... + n) = 1/2 * n * (n + 1), you get (note that n = 7 in your case):
$$W_t = 1.5 \times 9.81 \times \frac{1}{2} \times 8 \times 7$$
which you can re-order to give the expression you had.