In the figure,two identical springs have unstretched lengths of 0.25 m and spring constants of 300 N/m.The springs are attached to a small cube and stretched to a length L of 0.36 m as in Figure A.An external force P pulls the cube a distance D = 0.020 m to the right and holds it there.(See Figure B.)The work done by the external force P in pulling the cube 0.020 m is closest to
A) 0.12 J.
B) 0.060 J.
C) 6.0 J.
D) 12 J.
E) 0.80 J.

Question

In the figure,two identical springs have unstretched lengths of 0.25 m and spring constants of 300 N/m.The springs are attached to a small cube and stretched to a length L of 0.36 m as in Figure A.An external force P pulls the cube a distance D = 0.020 m to the right and holds it there.(See Figure B.)The work done by the external force P in pulling the cube 0.020 m is closest to 
A) 0.12 J. 
B) 0.060 J. 
C) 6.0 J. 
D) 12 J. 
E) 0.80 J.

Quizplus · Accepted Answer

The potential energy stored in a spring is given by $U=\frac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is the displacement from the equilibrium position. 
At equilibrium, the cube is pulled to the right by an external force $P$ such that the displacement is $D=0.020 	ext{ m}$.
The total displacement of the spring is $L+D=0.36+0.020=0.380 	ext{ m}$.
The potential energy stored in one spring is then $U=\frac{1}{2}(300)(0.380/2-0.25)^2=0.01155 	ext{ J}$.
The potential energy stored in both springs is $2U=0.0231 	ext{ J}$.
The work done by the external force $P$ is equal to the increase in potential energy of the springs, which is $\Delta U=0.0231 	ext{ J}$. 
Therefore, the closest choice for the work done by the external force $P$ is A) 0.12 J.

In the Figure,two Identical Springs Have Unstretched Lengths of 0