# Two Dimensional Motion and Conservation of Energy

#### Summary

In this physics lab students look at conservation of energy to find the horizontal velocity of a sphere in order to predict where it will land.

## Learning Goals

Students will identify the energy transfer. They will find the relationship between Potential Energy at the top of a ramp and Kinetic Energy at the bottom. Knowing the kinetic energy at the bottom, students can find the horizontal velocity of the sphere. After calculating the time the sphere is in the air students will predict where it will land.

## Context for Use

This lab is for a senior high class in Physical Science. It is conducted inside and will take a minimum of two days. Students need to know about projectile motion and be able to calculate how long a falling object is in the air. Then they can calculate how far that same object will travel horizontally. The lab can be used after an introduction of potential and kinetic energy.

**Subject**: Physics:Classical Mechanics:Work and Energy

**Resource Type**: Activities:Lab Activity

**Grade Level**: High School (9-12)

## Description and Teaching Materials

Given a curved ramp in which a sphere is rolled and leaves the edge of a lab table horizontally, students predict where the sphere will land. This is accomplished by recognizing that a fraction of the potential energy at the top of the ramp is in the form of kinetic energy at the bottom of the ramp. Knowing the kinetic energy at the bottom of the ramp students can find the horizontal velocity of the sphere. By measuring the distance the sphere falls after it leaves the ramp students can calculate the time the sphere is in the air. Knowing the horizontal velocity and the time students can calculate the horizontal distance the sphere travels and predict where the sphere will land.

Day 1

Not all the P.E at the top of the ramp is transformed to K.E. at the bottom. A good discussion is the other energy transformations that are occurring. Talk about friction, heat, and rotational K.E. vs translational K.E. The goal of Day 1 is to find the fraction of P.E. at the top of the ramp that winds up in the form of translational K.E. at the bottom. (P.E. at the top)(fraction)=(K.E. at the bottom) therefore the fraction=(K.E. at the bottom)/(P.E. at the top)(fraction).

Day 2

The height of the ramp is adjusted. Student find the P.E. at the top of the ramp and use the fraction to predict the K.E. at the bottom. Knowing the K.E. find the velocity, knowing the velocity and time in the air find the horizontal displacement and predict the landing spot. Brief Power Point of Lab (PowerPoint 82kB Aug24 07) Day 1 Work Sheet (Microsoft Word 34kB May16 11)

Day 1

Not all the P.E at the top of the ramp is transformed to K.E. at the bottom. A good discussion is the other energy transformations that are occurring. Talk about friction, heat, and rotational K.E. vs translational K.E. The goal of Day 1 is to find the fraction of P.E. at the top of the ramp that winds up in the form of translational K.E. at the bottom. (P.E. at the top)(fraction)=(K.E. at the bottom) therefore the fraction=(K.E. at the bottom)/(P.E. at the top)(fraction).

Day 2

The height of the ramp is adjusted. Student find the P.E. at the top of the ramp and use the fraction to predict the K.E. at the bottom. Knowing the K.E. find the velocity, knowing the velocity and time in the air find the horizontal displacement and predict the landing spot. Brief Power Point of Lab (PowerPoint 82kB Aug24 07) Day 1 Work Sheet (Microsoft Word 34kB May16 11)

## Teaching Notes and Tips

This is a very open ended and student driven activity. Allow the students to struggle with derivations. I do ask for the notes demonstrating their work and quiz them on the physics concepts. The bulk of the grade is their ability to place a coin on the floor and hit it with the sphere. I give students only one chance. This motivates them to focus on details.

## Assessment

Student show their derivation to find the fraction.

Students show their derivation for finding the final horizontal distance the sphere travels.

Students take a quiz on the lab.

Students roll the sphere and hit a target. I use concentric 1 cm circles.

Students show their derivation for finding the final horizontal distance the sphere travels.

Students take a quiz on the lab.

Students roll the sphere and hit a target. I use concentric 1 cm circles.

## Standards

Physical Science 9-12

Energy Transformations

Motion

Energy Transformations

Motion