Pull the knob and let go. Something was stored while you pulled. That is today's question.

Energy in Elastic Systems

How hard is it to stretch a spring, and where does the energy go?

Unit 4, Lab 1

Name Date Period

Before you collect anything

1.Your group has been given a particular spring. Pull it gently on the virtual bench in the Data section. What is the relationship you expect between how far you stretch it and how hard you have to pull? Sketch it.

Draw your own axes and label them.

Can't draw it well here? Describe your sketch in words (this is also what gets sent when you submit).

2.Where is the energy going while you stretch it? Draw an energy pie chart for the spring before you pull and while you are holding it stretched.

The system is the spring. The area of the whole pie stands for the total energy stored in the system, so a bigger pie means more energy. Drag the sliders to build each pie.

In a sentence or two, explain how your two pies differ and where the new energy came from.

Apparatus

Your assigned spring, chosen by letter on the virtual bench. Your teacher gives you the letter. Do not switch to another letter, because the whole class needs different springs.
A virtual force sensor, attached to the free end of the spring
A virtual ruler with a millimeter scale, plus a zoom view of the free end of the spring
A virtual stand and clamp that hold the fixed end of the spring for you

Two rules that protect the data and the equipment

Do not over-stretch the spring. Once a spring is pulled past its limit it never goes back. That is true of the virtual spring too: it stays stretched out, or it breaks, and you have to swap in a replacement and re-measure. If the coils start separating unevenly, let go.

Do not record a data point for an unstretched spring. The 0,0 point is not data. It is an assumption, and forcing your line through it hides one of the most interesting things this lab can show you.

Procedure

The virtual clamp holds one end of the spring so it cannot move. With nothing pulling the spring, read its length on the ruler. This is your reference length.
Pull the free end by dragging the force sensor. Hold it still, then read the force on the sensor and read the new length on the ruler (the zoom view shows the millimeter marks).
The stretch is the new length minus the reference length. It is a change, not a total.
Repeat for at least six different stretches, spread across the range your spring can take safely.

Data

The virtual bench

Your spring (your teacher gives you a letter)

Do not switch springs after you start. Other groups need the other springs.

Drag the force sensor to pull the spring, or use the buttons. The spring stays where you put it until you press Let go. Read the length where the red line meets the ruler, in the zoom view. The sensor reading has a little noise, like a real one.

Your measurements

Reference length of unstretched spring (m)

Enter every length in meters. The check column tells you if a row agrees with itself and with your spring. If it flags a row, read the ruler and the sensor again.

Run	Length (m)	Stretch x (m)	Force F (N)	Check

Graph

Plot force against stretch, with stretch on the horizontal axis. Your points appear as you fill in the table. Label both axes with a quantity and a unit, then drag the two handles to place a best-fit line. Do not force your line through the origin.

Horizontal axis label Vertical axis label

Keyboard: Tab to a handle, then use the arrow keys (Shift for bigger steps).

Analysis

1.Find the slope of your line. Show two points, the subtraction on the top and on the bottom, and the units.

Point 1 (on your line) x₁ (m) F₁ (N)

Point 2 (on your line) x₂ (m) F₂ (N)

Top: F₂ − F₁ (N) Bottom: x₂ − x₁ (m) Slope (number) Units

2.Say what your slope means in one sentence that does not use the word “slope.”

3.What is the vertical intercept of your line? If it is not zero, say what that means about your particular spring, physically.

Vertical intercept (number)Units

4.Write the equation of your line, with your numbers and their units in it.

F = slope units · x + intercept units

The energy question

This is your graph again. Use the buttons to shade regions on it. Move the line in the Graph section above if you need to.

5.Shade the area under your graph from a stretch of zero out to the largest stretch you measured. Calculate that area, and multiply the units as well as the numbers.

Show your work (shape, numbers, units)

Area (number)Units, multiplied out

6.What quantity did you just calculate? How do the units tell you?

7.Go back to your pie charts above. As the stretch doubles, what happens to the size of the pie? Answer from the area on your graph, not from memory.

8.Calculate the energy stored in stretching your spring the FIRST half of your maximum stretch, and then the energy stored in stretching it the SECOND half. Are they the same? Show both areas on the graph.

First half, 0 to ½ max (number) Second half, ½ max to max (number) Units Same?

Show your work and explain what you found

Turn it in

Make sure your name and period are filled in at the top, then press Submit to Mr. C. Mr. C gets a PDF of the text of your lab: your data, your line, and your written answers.

Your sketch, pies, and graph are pictures, and pictures don't go through Submit. Press Print or save as PDF to keep a copy that includes them. If Submit doesn't work, use Copy my lab and paste it into the Canvas assignment.