Question

4 big dictionaries, each 10.0 cm thick and each 1.50 kg, are resting side by side flat on a table 1.06 m high.

How much work would it take to stack them one atop the other?

How high would that raise the center-of-mass of all books?

Answer 1

$m = 1.5kg$

$d = 10cm = 0.1m$

$h_0 = 1.06m$

$g = 9.8\frac{m}{s^2}$

$\text{Move 2 dictionary to 1 dictionary:}$

$W_1 = mg*d$

$\text{Move 3 dictionary to a stack of 1 and 2 dictionaries}$

$W_2 = mg*2d$

$\text{\text{Move 4 dictionary to a stack of 1 and 2 and dictionaries}}$

$W_2 = mg*3d$

$W = W_1+W_2+W_3= mg*6d=1.5*9.8*6*0.1=8.82J$

$W = 4mg\Delta h_c$

$4m - \text{The total mass of dictionaries}$

$\Delta h_c - \text{changing the position of the center of gravity of dictionaries}$

$\Delta h_c=\frac{W}{4mg}=\frac{8.82}{4*9.8*1.5}=0.15m$

$\text{Answer:}W = 8.82J;\Delta h_c = 0.15m$