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How to Apply Hooke's Law to Make Your Own Spring Scale

Hooke's law states that when you stretch a spring, it will exert a restoring force (pull back against the stretch) in linear proportion to the distance you stretch it. In equation form, it's F = -kx, where F = the restoring force, x = the distance the string is stretched, and k = the spring constant (a number that depends on the material properties of the spring). The negative sign means that the restoring force points in the opposite direction from the stretch. Because every action has an equal and opposite reaction (Newton's Third Law of Motion), Hooke's law also means the amount of force with which you pull on a spring is linearly proportional to the distance it will stretch (F = kx). In other words, if you pull a spring twice as hard, it will stretch twice as far.

If you hang an object from the end of a spring, the force of gravity on that object will pull on the spring. Since the pull of gravity on an object is proportional to its mass, you can apply Hooke's law to figure out the mass of an object by hanging it from a spring -- making your own spring scale.

Things You'll Need

Metal spring
Screw eye
Hook and eye turnbuckle
Pliers
Drill
Drill bit slightly smaller than diameter of screw-eye-threaded end
2-by-4-inch board
Two sawhorses or tables
One small object whose mass you already know
Object of unknown mass
Ruler
Pencil or pen
Paper

Instructions

Construction
- 1
  Drill a small starter hole near the center of one wide side of the 2-by-4-inch board, using the drill and drill bit.
- 2
  Screw the screw eye into the starter hole by hand. Tighten it by hand as far as it will go. Clamp the pliers onto the screw eye and carefully tighten the screw eye a little more.
- 3
  Fasten one end of the metal spring to the screw eye, by bending it around the screw eye using the pliers.
- 4
  Fasten the eye end of the hook and eye turnbuckle to the free end of the spring, again by bending the spring around the eye with the pliers.
- 5
  Support the board at either end with the sawhorses or tables, so that the spring is hanging down from the screw eye.
Calibration
- 6
  Measure the length of the spring while it's hanging down with only the hook and eye turnbuckle attached. Write down the length.
- 7
  Hang the small object of known mass from the hook part of the turnbuckle. Wait for the spring to stop moving. Measure the length of the spring again with the small mass attached. Write down the length of the spring and the mass of the object. Remove the object from the hook.
- 8
  Compute the weight of the object. W = mg: weight equals mass times acceleration of gravity. On the earth's surface, g = 9.8 meters/second^2. The weight gives you the force (F) term in Hooke's law.
- 9
  Compute the difference in the length of the spring with and without the mass attached. This difference is the displacement (x) term in Hooke's law.
- 10
  Put your measured values for F and x into the Hooke's law equation, F = kx. (The negative sign isn't included here, because the force and the displacement are in the same direction.) Solve for the unknown k. Write down the value of k.
Using the Spring Scale
- 11
  Hang an object of unknown mass from the hook end of the turnbuckle.
- 12
  Measure the length of the spring with this object attached. Write down the length of the spring.
- 13
  Compute the difference in the length of the spring with the object attached, and the length of the spring with no object attached. This difference will be the displacement (x) term in the Hooke's law equation.
- 14
  Put your measured value for x, and your previously computed value for k, into the Hooke's law equation (F = kx). Solve for the unknown F. Write down the value of F. This is the weight of the object.
- 15
  Convert weight into mass by using the equation W = mg. Put in your measured weight of the object for W, and the constant value of g on the Earth's surface, 9.8 meters/second^2. Solve this for the unknown m. This gives you the mass of the object.

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