College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Question
Needing these tables filled in for Vfinal, UGinitial, K final, and %diff
![Certainly! Here's a transcription of the document that could be used on an educational website:
---
**Lab: Conservation of Mechanical Energy**
**Name:** [Hannah Ball]
**Lab Section:**
**Date:**
**Introduction:**
An object that is dropped from a height has only potential energy (due to gravity) initially, but will have only kinetic energy when it reaches the bottom of its fall (height equals zero). During the free fall, potential energy (Ug) is converted into kinetic energy (K). The K gained during the fall will be equal to the Ug lost.
\[ \Delta K = -\Delta U_g \]
where, \[ U_g = mgh \quad K = \frac{1}{2}mv^2 \]
In part one, we will revisit an experiment that has already been performed: Acceleration Due to Gravity. A metal ball will be dropped at a certain height and its final velocity will be determined. The Ug of the ball initially will be compared to the K of the ball after a certain distance traveled. The final velocity of the ball, if dropped from rest, can be determined \((v_f = gt)\). Therefore, K becomes:
\[ K = \frac{1}{2}m(gt)^2 \quad \text{where t is the fall time.}\]
In part two, we will use an inclined air track. The glider will be placed near the top and allowed to accelerate down the incline through the photogate at the bottom. The vertical height the glider traveled will be used to determine the initial Ug. The photogate will record the time it takes the glider’s sail to pass through the IR beam. With this time and the width of the sail, an average velocity can be determined. With this velocity, the final K will be calculated.
The conversion of spring energy to kinetic energy will be demonstrated in part three. The spring constant for the rubber band of the glider will be determined. With the spring constant known, a predicted velocity of a more massive glider will be compared to the experimental velocity once the spring energy is converted into kinetic energy.
\[ \Delta U_s = -\Delta K \]
Where \[ U_s = \frac{1}{2}k∆x^2 \]
---
This transcription includes all the equations and outlines the objectives and methods of the experiment on the conservation of mechanical energy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa86b51e-2b65-4461-8808-00a090348d92%2F4baac0ac-0353-4a1b-8f81-b5394155c3de%2Flx9emlo.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here's a transcription of the document that could be used on an educational website:
---
**Lab: Conservation of Mechanical Energy**
**Name:** [Hannah Ball]
**Lab Section:**
**Date:**
**Introduction:**
An object that is dropped from a height has only potential energy (due to gravity) initially, but will have only kinetic energy when it reaches the bottom of its fall (height equals zero). During the free fall, potential energy (Ug) is converted into kinetic energy (K). The K gained during the fall will be equal to the Ug lost.
\[ \Delta K = -\Delta U_g \]
where, \[ U_g = mgh \quad K = \frac{1}{2}mv^2 \]
In part one, we will revisit an experiment that has already been performed: Acceleration Due to Gravity. A metal ball will be dropped at a certain height and its final velocity will be determined. The Ug of the ball initially will be compared to the K of the ball after a certain distance traveled. The final velocity of the ball, if dropped from rest, can be determined \((v_f = gt)\). Therefore, K becomes:
\[ K = \frac{1}{2}m(gt)^2 \quad \text{where t is the fall time.}\]
In part two, we will use an inclined air track. The glider will be placed near the top and allowed to accelerate down the incline through the photogate at the bottom. The vertical height the glider traveled will be used to determine the initial Ug. The photogate will record the time it takes the glider’s sail to pass through the IR beam. With this time and the width of the sail, an average velocity can be determined. With this velocity, the final K will be calculated.
The conversion of spring energy to kinetic energy will be demonstrated in part three. The spring constant for the rubber band of the glider will be determined. With the spring constant known, a predicted velocity of a more massive glider will be compared to the experimental velocity once the spring energy is converted into kinetic energy.
\[ \Delta U_s = -\Delta K \]
Where \[ U_s = \frac{1}{2}k∆x^2 \]
---
This transcription includes all the equations and outlines the objectives and methods of the experiment on the conservation of mechanical energy.
![**Results Page:**
**Date:** 10/18/2020
**Lab Section:** [Blank]
---
**Table 1: Potential to Kinetic Energy During Free Fall**
| Mass | Height | t1 | t2 | t3 | t_avg | V_final |
|-------|--------|--------|--------|--------|-------|---------|
| 16.1 g| 141.1 cm | 0.547 s | 0.574 s | 0.571 s | 0.574 s | [Blank] |
**Energy Table #1**
| | Ug_initial | K_final | %diff |
|-----------|------------|--------|-------|
| [Blank] | [Blank] | [Blank]| [Blank]|
**Calculations:**
[Blank]
---
**Table 2: ΔE Along an Incline**
| Mass | Sail distance | Initial height | Final height | Δheight | time | V_final |
|---------|---------------|----------------|--------------|---------|------|---------|
| 200.8 g | 10 cm | 32.2 cm | 16.3 cm | [Blank] | 0.172 s | [Blank]|
**Energy Table #2**
| | Ug_initial | K_final | %diff |
|-----------|------------|---------|-------|
| [Blank] | [Blank] | [Blank] | [Blank]|
**Calculations:**
[Blank]
---
**Explanation:**
The document contains two primary tables illustrating experimental data for energy transformations. The first table tracks the transition of potential energy to kinetic energy during a free fall, measuring mass, height, and time intervals. The second table examines energy changes along an incline with recorded mass, distances, and heights. Calculations for energy differences and percentages are outlined but not detailed in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa86b51e-2b65-4461-8808-00a090348d92%2F4baac0ac-0353-4a1b-8f81-b5394155c3de%2F3sadn18.jpeg&w=3840&q=75)
Transcribed Image Text:**Results Page:**
**Date:** 10/18/2020
**Lab Section:** [Blank]
---
**Table 1: Potential to Kinetic Energy During Free Fall**
| Mass | Height | t1 | t2 | t3 | t_avg | V_final |
|-------|--------|--------|--------|--------|-------|---------|
| 16.1 g| 141.1 cm | 0.547 s | 0.574 s | 0.571 s | 0.574 s | [Blank] |
**Energy Table #1**
| | Ug_initial | K_final | %diff |
|-----------|------------|--------|-------|
| [Blank] | [Blank] | [Blank]| [Blank]|
**Calculations:**
[Blank]
---
**Table 2: ΔE Along an Incline**
| Mass | Sail distance | Initial height | Final height | Δheight | time | V_final |
|---------|---------------|----------------|--------------|---------|------|---------|
| 200.8 g | 10 cm | 32.2 cm | 16.3 cm | [Blank] | 0.172 s | [Blank]|
**Energy Table #2**
| | Ug_initial | K_final | %diff |
|-----------|------------|---------|-------|
| [Blank] | [Blank] | [Blank] | [Blank]|
**Calculations:**
[Blank]
---
**Explanation:**
The document contains two primary tables illustrating experimental data for energy transformations. The first table tracks the transition of potential energy to kinetic energy during a free fall, measuring mass, height, and time intervals. The second table examines energy changes along an incline with recorded mass, distances, and heights. Calculations for energy differences and percentages are outlined but not detailed in the image.
Expert Solution
Step 1:
vf = gt
vf = (9.8)(0.5452)
vf = 5.34296 m/s
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