**Hooke's Law & Spring Constants (k)**

**Obj: **Determine relationship between Force and Distance
(x) for a spring,

and the Force Constant (k) of a Spring.

**Materials**: spring, four slotted masses, meter stick,
unknown mass, “big” spring

**Methods**

1.
Sketch the set up.

2. Record the
“rest” position of the spring (let x_{o} = 0.0 cm).

3.
Add a 50, or 100 g mass to extend the spring beyond its
rest position (x_{o}); record the mass, and the Δx.

4. Repeat for** **3
more masses, adding the total of the masses and total Δx.

5. Move to another
station with a different spring and repeat the procedure.

**Analysis**

1.
For each spring, plot a graph of Force (N) vs. distance (Δx).
Let g = 10 m/s^{2} when converting the masses to
Newtons.

2. Determine the
slope (k) of the line. What
are the units and what does the slope represent?

3. Calculate the
energy in Joules for *one* of your springs at the various
Δx’s. Plot
this energy on the same graph by using a double scale as
described.

4. Compare your
force constants and draw a conclusion about the magnitude of the
force constant k and the "stretchability" of a spring.

5. Write an equation
relating Force (F), displacement (Δx), and the force
constant of a spring (k). State
Hooke's Law in a sentence.

6. Calculate the
spring constant of the “big” spring, if available.

7. Describe the
mathematical relationship of the PE_{s} in a spring to
its stretch.

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