6.28. To stretch a spring 3.00 cm from its unstretched length, 12.0 J of work must be done. (a) What is the force constant of this spring? (b)What magnitude force is needed to stretch the spring 3.00 cm from its unstretched length? (c) How much work must be done to compress this spring 4.00 cm from its unstretched length, and what force is needed to stretch it this distance? Identify: The work that must be done to move the end of a spring from x1 to x2 is W 12 kx22 12 kx12 Fx kx . The force required to hold the end of the spring at displacement x is . Set Up: When the spring is at its unstretched length, x 0 . When the spring is stretched, x 0 , and when the spring is compressed, x 0 . Execute: (a) x1 0 and W 12 kx22 k . 2W 2(12.0 J) 2.67 104 N/m x22 (0.0300 m)2 . 4 (b) Fx kx (2.67 10 N/m)(0.0300 m) 801 N . (c) x1 0 , x2 0.0400 m . Fx kx (2.67 104 N/m)(0.0400 m) 1070 N W 12 (2.67 104 N/m)(0.0400 m)2 21.4 J . . Evaluate: When a spring, initially unstretched, is either compressed or stretched, positive work is done by the force that moves the end of the spring.