Question #204752

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.


1
Expert's answer
2021-06-09T08:06:08-0400

ht=1mh_t=1m

hd=10cm=0.1mh_d=10cm =0.1m

n=5n=5

P=25NP=25N

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

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

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

Ep0=nP(ht+hd2)E_{p0}= n*P*(h_t+\frac{h_d}{2})

Ep0=525(1+0.05)=131.25JE_{p0}= 5*25*(1+0.05)=131.25J

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

hc=ht+nhd2h_c=h_t+\frac{n*h_d}{2}

hc=1+50.12=1.25mh_c=1+\frac{5*0.1}{2}=1.25m

Ep1=nPhcE_{p1}=n*P*h_c

Ep1=5251.25=156.25JE_{p1}=5*25*1.25=156.25J

W=Ep1Ep0W= E_{p1}-E_{p0}

W=156.25131.25=25JW= 156.25-131.25=25J

Answer: W=25J\text{Answer: }W=25J



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