## Extra Credit 6

In this exercise you will verify Hooke's law for a real spring and determine the spring constant of the spring.  You also will explore a spring simulation.

Go to Canvas, Assignments, Extra Credit 6 and answer the questions in blue font.

### Part 1

One end of a spring is attached to a rigid support.
Different weights are hung on the other end, and the spring stretches to different lengths.

Procedure:

• In the pictures below measure the position of the free end of the spring as a function of the applied force.  Always measure the position of the same physical point.
• Measure the position in units of meter and the force in units of Newton.  Enter your data into a spreadsheet.  Your first rows should look similar to this.
 position (m) force (N) 0.22 0.1 0.255 0.2
• Use the spreadsheet to plot the applied force versus the position of the free end of the spring.
Scatter plot:  Vertical axis: force,  Horizontal axis: position.
• Use the spreadsheet's trendline to determine slope of the straight line that best fits the data.  Format the trendline label to show a number with at least 2 decimal places.
Since Fapplied = kx, ∆Fapplied = k∆x, and the slope of the straight line will be equal to the spring constant k.
What is the value of k (magnitude and units)?
What is the equilibrium position of the free end of the spring in units of cm, i.e. in your graph, what is x (in cm) when y = 0?
• Make a prediction.  If the position of the free end of the spring would be at 1.05 m, what would be the applied force?

### Part 2:

Link to the simulation: http://phet.colorado.edu/simulations/sims.php?sim=Masses_and_Springs

#### Explore the interface!

• You can click and drag a mass to the bottom of a spring and it will hook onto the spring.
• You can click and drag the horizontal (dotted) line to a new position.
• You can click and drag the vertical ruler to a new position.
• In the green control box you can choose operating parameters.
• You can display the components of the energy of one of the mass/spring systems.
• You can turn on a stopwatch.
• You can pause or slow down the motion.
• You can move the mass-spring system to a different location, for example the Moon.
• You can move a slider to change the stiffness of of spring 3.
• You can change the amount of friction in the system.

#### Experiment:

There are three unlabeled masses colored red, gold, and green.  Design an experiment to determine those masses.  What is the mass (in g) of the golden mass?

Move the setup to the surface of Planet X.  Given g = 9.8 m/s2 near the surface of Earth, design an experiment to determine those gravitational acceleration g' near the surface of planet X.  What is g' in units of m/s2?