Student Exploration: Period of Mass on a Spring
Vocabulary: oscillate, period, spring, spring constant
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
Frank has a mass of 100 kg, and his petite wife, Jo, has a mass of 50 kg. While on vacation, they decide to try bungee jumping. Frank nearly touches the ground on his jump, and he bounces up and down six times in 30 seconds.
How far do you think Jo will fall, compared to Frank?
In 30 seconds, do you think Jo will bounce up and down more times or fewer times than Frank?
A bungee cord is a type of spring because it is elastic—the more it is stretched, the greater the force pulling it back. If you hang a weight on a spring, pull the weight down and let go, the weight will move up and down, or oscillate, for quite a while. The time it takes for one complete down and up motion is called the period of the spring.
With the Period of Mass on a Spring Gizmo™, you will measure the effects of three variables on the period of a spring: mass (m), the spring constant (k), and gravitational acceleration (g). First, practice measuring the period.
Check that the mass (m) is 1.0 kg, the spring constant (k) is 100.0 N/m, and gravitational acceleration (g) is 9.8 m/s2. On the bottom of the Gizmo, click on the POINTER button and drag an arrow so that its tip just touches the blue bob on the bottom of the spring, as shown.
Select the TABLE tab. When the bob touches the arrow, click Mark time. Count ten touches and click Mark time again.
What is this time?
Divide this time by 10 to find the period of the spring. What do you get?
Get the Gizmo ready:
Click Reset. Set m to 0.2 kg.
Check that k is 100 N/m andg is 9.8 m/s2.
Question: How does mass affect the period of a spring?
Predict: How do you think increasing mass will affect the period of a spring?
Gather data: Adjust the arrow to mark the bottom of the spring’s motion. For each given mass, measure the time for ten oscillations and divide this number by 10 to find the period. (Keep k set to 100 N/m and g set to 9.8 m/s2 in each experiment.)
Observe: In general, how does increasing the mass affect the period of the spring?
Analyze: Divide the period for the 0.8 kg mass by the period for the 0.2 kg mass.
What is the effect of multiplying the mass by 4?
Divide the period for the 1.8 kg mass by the period for the 0.2 kg mass. What is the effect of multiplying the mass by 9?