Question

What is the potential energy stored in a spring that has a restoring force of 1kN/m and has been stretched by 1 cm? Hints: Potential Energy =FS (force x distance stretched)
A. 1J
B. 10J
C. 100J
D. 1000J
E. No correct answer is available

Answer 1

You're teacher's hint is faulty. Let me explain.

From the Work-Energy Theorem, we know that\[W = \Delta E = \Delta KE + \Delta PE\]This states that work equals the change in energy. In this case, we can say that \(\Delta KE = 0\).

Additionally, we know that the definition of work is\[W = \int\limits F \cdot dx\]The force of a spring is\[F_s = kx\]\[\therefore W = \int\limits kx dx\]Integrating obtains\[W = {1 \over 2} kx^2\]

Therefore, we can express the potential energy of the spring as\[W =\Delta PE \rightarrow PE_s = {1 \over 2} kx^2\]where k is the spring constant (units of N/m) and x is the displacement (units of m). This will give you units of Joules.