Hooke's Law

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Introduction

Hooke's law

Where F is the restoring force, k is the spring constant andx is the displacement. Higher value of spring constant means it is harder to stretch a spring versus soft spring where the application of little force will produce a large stretch. Plotting Force versus displacement of two springs with two different spring constants will illustrate the point.

Potential Energy of a spring-object system is:

Objectives:

Following aspects of Hooke's law are investigated through the simulation:

1. relationship of force (F) with stretch or compression of a spring (displacementx)
2. potential energy as a function of displacement

Experiment:

When you click on the link, you will see the simulation of the Hooke's law. There are three tabs: Intro, Systems and Energy. The lab uses a simulation developed by University of Colorado at Colorado Boulder

Click to start the simulation

1. Click "Intro". Choose a spring constant (k) constant below 500 N/m (different than 200N/m). Click all - Applied force, Spring force, Displacement, Equilibrium position and values. Use the red bar to move away from zero; for example, at applied force of 18 N, the displacement is 0.090 m and at that stretch, applied force and spring force are equal.

Force (N)	Displacement (m)

Change the spring constant to a value higher than 500N/m.

Force (N)	Displacement(m)

1. Plot the Force (y-axis) vs displacement (x-axis) on EXCEL or on piece of paper. Label the axes and include the units.

Insert the graph (Excel or picture) in the space below:

2. Find the spring constant for the spring in Newton/meters from the slopethe graph.

3. What forces will stretch each spring for 0.3 m?

1. Click" Energy". Choose k=400N/m, select "Energy Plot", "Applied Force", "Displacement", "Equilibrium Position". Move the slide of displacement from 0 to maximum on both the positive and negative side.

1. What is the maximum potential energy? Was it for the positive or negative displacement?
2. What is the minimum potential energy?
3. What is the value of displacement when the energy is half of the maximum value?
4. What is the value of energy when the displacement is half of the maximum value?

1. Problem:

A student measured 15s for the 20 complete oscillations for an object of 200g attached at the free end of a spring. Calculate the period of oscillation (T) and the spring constant (k). Write the equation used and then the numerical values.