 #### Advanced Physics Through Inquiry 1 Teacher Guide

(PS-2848) Teacher guide featuring 15 labs designed for Advanced Placement Physics 1.

### Periodic Motion: Mass and Spring

#### Lab Summary

Students use a motion sensor to determine the physical properties of a hanging mass and spring system that affect its period of oscillation, and then use their data to support a mathematical model relating period, mass, and spring constant.

#### Theory

What variables affect the period of oscillation of a mass and spring system? Experimentally determine the physical properties of a hanging mass and spring system that affect its period of oscillation.

#### Method

The Structured version of this lab activity is divided into four parts: Part 1 – Students assemble a vertical mass and spring system and then displace the mass vertically to set the system into oscillatory motion. Students measure the period Ts of their system as it oscillates, while increasing the initial vertical displacement of the mass in each trial. They measure the time for ten cycles of motion in each trial and use this time to determine the average period of the system. Student data will show that the average period in each trial is identical, or nearly identical, prompting students to recognize that the period of a mass and spring system is unaffected by changes in initial vertical displacement. Part 2 – Using the same setup as in Part 1, students measure the average period of two mass and spring systems with identical spring constant and hanging mass, but different length. Student data will show that the average period for each system is identical, or nearly identical, prompting students to recognize that the period of a mass and spring system is unaffected by the length of the system. Part 3 – Using the same setup as in Part 1, students measure the average period of three mass and spring systems with identical length and mass, but different spring constant. Students calculate 1/√spring constant for each system, and then plot a graph of period versus 1/√spring constant. The plot of period versus 1/√spring constant will show a linear (proportional) relationship. Students are expected to recognize that the period of a mass and spring system is proportional to the inverse square root of the spring constant. Part 4 – Using the same setup as in Part 1, students measure the average period of a mass and spring system while increasing the amount of hanging mass in each trial. Students calculate √mass for each trial, and plot a graph of period versus √mass. The plot of period versus √mass will show a linear (proportional) relationship. Students are expected to recognize that the period of a mass and spring system is proportional to the square root of the hanging mass value. Combining the results of all four parts of the lab activity, students use their data to support the actual mathematical relationship between period, mass, and spring constant for a mass and spring system.

#### PASPORT Motion Sensor

(PS-2103A) The PASPORT Motion Sensor accurately measures position, velocity, and acceleration of a target. Can be used to track the motion of carts, balls, people and more.

#### Demonstration Spring Set

(ME-9866) Four large springs ideal for Hooke's Law or Conservation of Energy demonstrations.

#### Aluminum Table Clamp

(ME-8995) This clamp with 6.5 cm grip width, accepts plain or threaded rods up to 1/2 inch or 1.25 cm.

#### 90 cm Stainless Steel Rod

(ME-8738) Non-threaded and non-magnetic lab rod.

#### 45 cm Stainless Steel Rod

(ME-8736) Non-threaded and non-magnetic lab rod.

#### Right Angle Clamp

(SE-9444) This clamp fits rods up to 18 mm (11/16 in) in diameter.

#### Hooked Mass Set

(SE-8759) A rugged cast-iron mass set that is coated with enamel.

#### Four Scale Meter Stick

(SE-8695) A convenient measuring device that includes four different metric scales of various precision.

Tape

#### Advanced Physics 1 Starter Bundle

(PS-2815) Equipment and sensor starter bundle for performing 8 experiments in the Advanced Physics through Inquiry 1 Teacher Guide.

### Interface Required

This experiment may require software and an interface for data collection.