Answer to Question #204752 in Classical Mechanics for Hana

Question

Five thick dictionaries each 10cm thick and each weighting 25N,are resting side by side flat on a table 1m high.how much work would be done against gravity to stack one on top of the other.

Answer 1

$h_t=1m$

$h_d=10cm =0.1m$

$n=5$

$P=25N$

$\text{Potential energy of dictionaries lying on the table.}$

$\text{It is assumed that the dictionary is homogeneous and the height of the center}$

$\text{of gravity is half the width of the dictionary:}$

$E_{p0}= n*P*(h_t+\frac{h_d}{2})$

$E_{p0}= 5*25*(1+0.05)=131.25J$

$\text{The center of gravity of the stack of dictionaries on the table:}$

$h_c=h_t+\frac{n*h_d}{2}$

$h_c=1+\frac{5*0.1}{2}=1.25m$

$E_{p1}=n*P*h_c$

$E_{p1}=5*25*1.25=156.25J$

$W= E_{p1}-E_{p0}$

$W= 156.25-131.25=25J$

$\text{Answer: }W=25J$