A student is about to launch a 0.2kg rock from a sling shot as shown. The natural length of the spring is shown in the insert. The initial time is defined as just before the launch when the student has pulled the rock backwards and is holding the rock at rest with a 100N force (note that the natural and stretched total band lengths are shown). The final time is defined immediately after the launch. Neglect loss. 0.17m How much did the student change the length of the bands when she pulled the rock backwards? 0.58m What is the effective spring constant of the slingshot bands? reference level unit List the energy types at the initial and final time and whether work and loss (due to non- conservative forces) occur as well as the corresponding amounts of energy. initial: ЕРЕ work? no work J loss? no loss final: KE How fast will the rock be launched? m/s
A student is about to launch a 0.2kg rock from a sling shot as shown. The natural length of the spring is shown in the insert. The initial time is defined as just before the launch when the student has pulled the rock backwards and is holding the rock at rest with a 100N force (note that the natural and stretched total band lengths are shown). The final time is defined immediately after the launch. Neglect loss. 0.17m How much did the student change the length of the bands when she pulled the rock backwards? 0.58m What is the effective spring constant of the slingshot bands? reference level unit List the energy types at the initial and final time and whether work and loss (due to non- conservative forces) occur as well as the corresponding amounts of energy. initial: ЕРЕ work? no work J loss? no loss final: KE How fast will the rock be launched? m/s
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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![**Projectile Launching using a Slingshot: A Physics Exercise**
---
A student is about to launch a 0.2 kg rock from a slingshot as shown in the diagram. The natural length of the slingshot’s band is provided in the inset. The initial time is defined as just before the launch when the student has pulled the rock backward and is holding the rock at rest with a 100 N force. Note that the natural and stretched total band lengths are shown. The final time is defined immediately after the launch. Ignore any loss of energy due to non-conservative forces.
### Key Measurements:
1. **Natural Length of Slingshot Band:**
- 0.17 meters
2. **Stretched Length at Full Extension:**
- 0.58 meters
### Questions and Calculations:
#### 1. Change in Length of Bands:
How much did the student change the length of the bands when she pulled the rock backward?
\[
\Delta L = 0.58\, \text{m} - 0.17\, \text{m} = 0.41\, \text{m}
\]
#### 2. Effective Spring Constant:
What is the effective spring constant (k) of the slingshot bands?
Using Hooke’s Law:
\[
F = k \Delta L \implies k = \frac{F}{\Delta L}
\]
\[
k = \frac{100\, \text{N}}{0.41\, \text{m}} \approx 243.9 \, \text{N/m}
\]
#### 3. Energy Consideration:
| Initial | Value | Final | Value | Work | Value | Loss | Value |
|--------------------|------------------|---------------------|------------------|------------------------------|-------------------|------------------------------|-------------------|
| Elastic Potential Energy (EPE)| \(\frac{1}{2} k (\Delta L)^2\) | Kinetic Energy (KE) | \(\frac{1}{2} mv^2\) | No Work | 0 J | No Loss | 0 J |
Substitute \(k = 243.9 \, \text{N/m}\), \(\Delta L = 0.41 \, \text{m}\):
\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40d81c3d-217c-474a-b6c2-74f4c4a8c8c0%2Fc16bbb19-0d5d-422f-97f7-69a0134a07fb%2Fznw99sp_processed.png&w=3840&q=75)
Transcribed Image Text:**Projectile Launching using a Slingshot: A Physics Exercise**
---
A student is about to launch a 0.2 kg rock from a slingshot as shown in the diagram. The natural length of the slingshot’s band is provided in the inset. The initial time is defined as just before the launch when the student has pulled the rock backward and is holding the rock at rest with a 100 N force. Note that the natural and stretched total band lengths are shown. The final time is defined immediately after the launch. Ignore any loss of energy due to non-conservative forces.
### Key Measurements:
1. **Natural Length of Slingshot Band:**
- 0.17 meters
2. **Stretched Length at Full Extension:**
- 0.58 meters
### Questions and Calculations:
#### 1. Change in Length of Bands:
How much did the student change the length of the bands when she pulled the rock backward?
\[
\Delta L = 0.58\, \text{m} - 0.17\, \text{m} = 0.41\, \text{m}
\]
#### 2. Effective Spring Constant:
What is the effective spring constant (k) of the slingshot bands?
Using Hooke’s Law:
\[
F = k \Delta L \implies k = \frac{F}{\Delta L}
\]
\[
k = \frac{100\, \text{N}}{0.41\, \text{m}} \approx 243.9 \, \text{N/m}
\]
#### 3. Energy Consideration:
| Initial | Value | Final | Value | Work | Value | Loss | Value |
|--------------------|------------------|---------------------|------------------|------------------------------|-------------------|------------------------------|-------------------|
| Elastic Potential Energy (EPE)| \(\frac{1}{2} k (\Delta L)^2\) | Kinetic Energy (KE) | \(\frac{1}{2} mv^2\) | No Work | 0 J | No Loss | 0 J |
Substitute \(k = 243.9 \, \text{N/m}\), \(\Delta L = 0.41 \, \text{m}\):
\
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