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Author:
Jack Bauer

Student Exploration: Determining a Spring Constant

Vocabulary: displacement, equilibrium, Hooke’s law, restoring force, slope, spring, spring constant, weight

Prior Knowledge Questions (Do these BEFORE using the Gizmo.)

At the grocery store, you put a watermelon on a produce scale. This causes the spring to stretch as shown. How far will the spring stretch if you add another watermelon of equal mass?

What property allows springs to be used in scales?

Gizmo Warm-up

When you put a grapefruit on a grocer’s scale, the scale may bounce up and down a bit, but eventually it settles into an equilibrium state. At this point, the force pulling the spring down is equal to the restoring force pulling the spring up. You can explore these forces in the Determining a Spring Constant Gizmo™.

To begin, check that Spring 1 is chosen and nothing is hanging from the spring.

What is the level of the bottom of the spring?

Place the scale on the bottom of the spring. The scale has a mass of 20 grams. Wait for the spring to stop moving. At this point it has reached equilibrium.

What is the level of the spring now?

How much did the spring stretch? This is the displacement of the spring.

Place mass C (20 grams) on the scale. What is the level of the spring?

What is the displacement of the spring?

Activity:

The spring constant

Get the Gizmo ready:

Remove all weights from Spring 1.

Select the TABLE tab.

Question: How is the displacement of a spring related to the weight it bears?

Predict: In this activity, you will create a graph of the displacement vs. the weight on the spring. What do you think this graph will look like?

Calculate: Place the 20-g scale on the spring.

Convert the mass of the scale in grams to kilograms by dividing by 1,000.

What is the mass of the scale in kg?

To find the weight of the scale, multiply the mass (in kg) by gravitational acceleration, 9.81 m/s2. (Note: The units for weight are kg·m/s2, or newtons (N)).

What is the weight of the scale in newtons?

Tutorial