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 compress it this distance?

Solution 32E Step 1 of 7: For a spring with force constant(k), the force for stretching or compressing the spring by x meters is given by F= kx…………..1 Where k is force constant and x is the stretching distance. Similarly for the same spring, the work done in stretching or compressing spring from x 1o x i2 given by, W= k2x ) 2 k(x 2 ……1..1 Step 2 of 7: 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 Here we need to calculate the force constant for a spring which stretches 3cm form unstretched position when 12J of work is done on it. Given data, Unstretched length,x 1 0 Stretched length,x2= 3 cm= 0.03 m Work done, W= 12 J To find, Force constant, k= Using x 1 0in equation 2, 1 2 W= k2x ) 2 Step 3 of 7: Solving for force constant, k= 2 W2 (2 ) Substituting W= 12J and x = 2.03 m k= 2 (12 2) (0.03 m) 4 k=2.67× 10 N/m Therefore, the force constant of the given spring is 2.67× 10 N/m. 4 Step 4 of 7: (b) What magnitude force is needed to stretch the spring 3.00 cm from its unstretched length Here we need to calculate the force we need to apply on the spring with force constant k =2.67× 10 N/m to stretch it by x=3cm. Given data, Force constant, k=2.67× 10 N/m4 Distance, x= 3cm = 0.03m To find, Force, F= Using equation 1, F= kx