Hello Grace,
The potential energy stored in a spring may be expressed as PE = (1/2)k(Δx)2, where k is the spring constant, and Δx is the change in the length of the spring from its equilibrium length (the length when it is neither stretched or compressed.)
a) Stretched 4.44cm from equilibrium.
Note that the spring constant is given in units of N/m (Newtons per meter), so Δx must be expressed in meters. We have k = 420.8N/m, and Δx = .0444m. Using the formula given above, the potential energy is
PE = (1/2)*420.8N/m*(.0444m)2
PE ≅ 0.41477N·m (Note that the units are N·m = J)
PE = 0.415J (rounded to 3 significant figures.)
b) Compressed 2.79cm from equilibrium.
For compression, we take Δx to be negative. We have Δx = -.0279m. Thus,
PE = (1/2)*420.8N/m*(-.0279m)2
PE = .164J (again to 3 significant figures.)
c) If the spring is unstretched (and, we assume, uncompressed), we have Δx = 0. From the formula, it is clear that PE = 0J.
Hope that helps. Let me know if you need any clarification. Thanks,
William
