A certain spring is used as a scale to find the weight of groceries. When you place exactly 1.0-kg of bananas on the spring and let them come to rest, it compresses 2.3-cm. When you place a watermelon of unknown mass on the spring and let it come to rest, it compresses 6.2-cm. A. Draw a free-body diagram for each case. B. Find the spring constant of the spring. k = 427 N/m C. Determine the mass of the watermelon. mw = 2.7 kg
A certain spring is used as a scale to find the weight of groceries. When you place exactly 1.0-kg of bananas on the spring and let them come to rest, it compresses 2.3-cm. When you place a watermelon of unknown mass on the spring and let it come to rest, it compresses 6.2-cm. A. Draw a free-body diagram for each case. B. Find the spring constant of the spring. k = 427 N/m C. Determine the mass of the watermelon. mw = 2.7 kg
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)...
Related questions
Question
Please use equations on equation sheet. Will Rate. Thanks
Transcribed Image Text:**Problem 3**
A certain spring is used as a scale to find the weight of groceries. When you place exactly 1.0-kg of bananas on the spring and let them come to rest, it compresses 2.3 cm. When you place a watermelon of unknown mass on the spring and let it come to rest, it compresses 6.2 cm.
A. Draw a free-body diagram for each case.
B. Find the spring constant of the spring. \( k = 427 \, \text{N/m} \)
C. Determine the mass of the watermelon. \( m_w = 2.7 \, \text{kg} \)
![### Newton's Laws and Energy Concepts
**Newton's Second Law and Momentum:**
\[
\Sigma \vec{F}_{\text{on obj}} = \frac{d\vec{p}_{\text{obj}}}{dt} = m_{\text{obj}} \vec{a}_{\text{obj}}
\]
- This equation represents Newton's second law in terms of momentum, where the net force on an object is equal to the derivative of its momentum over time, or the product of mass and acceleration.
**Gravitational and Spring Forces:**
\[
F^{G}_{E0} = m_0 g
\]
- The gravitational force on an object is represented by the product of its mass and the acceleration due to gravity.
\[
F^{C}_{S0} = k \Delta x
\]
- The force exerted by a spring is proportional to its displacement, where \( k \) is the spring constant.
**Work Done by a Force:**
\[
W_F = \int_{x_i}^{x_f} |\vec{F}| \cos \theta \, |d\vec{x}|
\]
- Work done by a force is the integral of the force along the path of displacement, considering the angle between force and displacement.
\[
W_F = |\vec{F}| \cos \theta |\Delta \vec{x}|
\]
- For constant forces, work can be simplified as the product of the force magnitude, the cosine of the angle between the force and displacement directions, and the magnitude of displacement.
**Friction and Thermal Energy:**
- If friction is present: \(\Delta E_{\text{th}} = |\vec{F}_{\text{friction}}| |\Delta \vec{x}|\)
- The thermal energy increase is due to the frictional force times the displacement.
**Conservation of Energy:**
\[
\Sigma E_{n,i} + W_{\text{ext}} = \Sigma E_{n,f}
\]
- The total initial energy plus external work equals the total final energy.
OR
\[
E_{\text{Mech},i} + W_{\text{ext}} = E_{\text{Mech},f} + \Delta E_{\text{Int}}
\]
- The initial mechanical energy plus work done by external forces equals the final mechanical energy plus internal energy changes.
**Mechanical Energy:**
\[](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe28b8fdf-2552-4f73-8b1c-90734de9299b%2Fb1ff10ee-2198-475c-a839-7b35f49d8aaf%2Faykc6fq_processed.png&w=3840&q=75)
Transcribed Image Text:### Newton's Laws and Energy Concepts
**Newton's Second Law and Momentum:**
\[
\Sigma \vec{F}_{\text{on obj}} = \frac{d\vec{p}_{\text{obj}}}{dt} = m_{\text{obj}} \vec{a}_{\text{obj}}
\]
- This equation represents Newton's second law in terms of momentum, where the net force on an object is equal to the derivative of its momentum over time, or the product of mass and acceleration.
**Gravitational and Spring Forces:**
\[
F^{G}_{E0} = m_0 g
\]
- The gravitational force on an object is represented by the product of its mass and the acceleration due to gravity.
\[
F^{C}_{S0} = k \Delta x
\]
- The force exerted by a spring is proportional to its displacement, where \( k \) is the spring constant.
**Work Done by a Force:**
\[
W_F = \int_{x_i}^{x_f} |\vec{F}| \cos \theta \, |d\vec{x}|
\]
- Work done by a force is the integral of the force along the path of displacement, considering the angle between force and displacement.
\[
W_F = |\vec{F}| \cos \theta |\Delta \vec{x}|
\]
- For constant forces, work can be simplified as the product of the force magnitude, the cosine of the angle between the force and displacement directions, and the magnitude of displacement.
**Friction and Thermal Energy:**
- If friction is present: \(\Delta E_{\text{th}} = |\vec{F}_{\text{friction}}| |\Delta \vec{x}|\)
- The thermal energy increase is due to the frictional force times the displacement.
**Conservation of Energy:**
\[
\Sigma E_{n,i} + W_{\text{ext}} = \Sigma E_{n,f}
\]
- The total initial energy plus external work equals the total final energy.
OR
\[
E_{\text{Mech},i} + W_{\text{ext}} = E_{\text{Mech},f} + \Delta E_{\text{Int}}
\]
- The initial mechanical energy plus work done by external forces equals the final mechanical energy plus internal energy changes.
**Mechanical Energy:**
\[
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON