A spring with spring constant k has two equal masses attached to its ends. The masses are pulled outward symmetrically, stretching the spring by a length x beyond its natural length. The work done by the spring on each mass is

Step-by-step solution

Let the total extension of the spring be x . The total work done by the spring on both masses is equal to the negative of the potential energy stored in the spring: W_ total = - 1 2 kx^2 Since the two masses are equal and are pulled symmetrically, the displacement of each mass is equal and opposite. The work done by the spring on each mass is identical. Let W be the work done by the spring on each mass. Then: 2W = W_ total = - 1 2 kx^2 W = - 1 4 kx^2 Alternatively, when the spring is stretched by a distance y , the