**Part IV. Design Problem – Tuning I: "70 in 7.0 ± 0.7"** **Objective:** Your goal is to use your rotating machine to lower a 50-gram mass, starting from rest, through a distance of 70 centimeters in a time of 7.0 ± 0.7 seconds. Use the second-step pulley. The only machine parameter that you can adjust is the location of the brass weights along the rod. **Schematic:** The schematic of the rotating machine includes: - A rod labeled 'L' with brass weights 'M' on either side, where 'D' denotes the adjustable distance from the rotation axis to the center of mass of each brass weight. - A pulley of radius 'r' connected to a 50-gram mass. - The setup is centered around the axle rotation axis. **The Theory:** To find the value of D, apply theoretical analysis as guided by the questions below: 1. **Calculate the acceleration \(a\) of the hanging mass.** \(a = \_\_\_\_\_\_\_\_\_\_ \, \text{m/s}^2\). 2. **Calculate the tension \(T\) in the thread.** - First, draw a free-body diagram for the hanging mass. - Then set up \(F = ma\) for the translational motion of the mass. \(T = \_\_\_\_\_\_\_\_\_\_ \, \text{N}.\) **Instructions for Rotational Motion Calculations** 1. **Calculate the torque (τ) on the pulley due to the tension T.** - Formula: τ = __________ Nm 2. **Calculate the angular acceleration (α) of the rotating system.** - Formula: α = __________ rad/s² 3. **Calculate the rotational inertia (I) of the system.** - Formula: I = __________ kg m² 4. **Calculate the contribution to I from the two brass weights.** - **Hint:** I = I_weights + I_rod + I_axle - I_weights = __________ kg m² 5. **Calculate D.** - Formula: D = __________ m These steps outline the process for determining various physical properties of a rotating system, starting with torque and progressing through angular acceleration and rotational inertia calculations, with a focus on contributions from different components.
**Part IV. Design Problem – Tuning I: "70 in 7.0 ± 0.7"** **Objective:** Your goal is to use your rotating machine to lower a 50-gram mass, starting from rest, through a distance of 70 centimeters in a time of 7.0 ± 0.7 seconds. Use the second-step pulley. The only machine parameter that you can adjust is the location of the brass weights along the rod. **Schematic:** The schematic of the rotating machine includes: - A rod labeled 'L' with brass weights 'M' on either side, where 'D' denotes the adjustable distance from the rotation axis to the center of mass of each brass weight. - A pulley of radius 'r' connected to a 50-gram mass. - The setup is centered around the axle rotation axis. **The Theory:** To find the value of D, apply theoretical analysis as guided by the questions below: 1. **Calculate the acceleration \(a\) of the hanging mass.** \(a = \_\_\_\_\_\_\_\_\_\_ \, \text{m/s}^2\). 2. **Calculate the tension \(T\) in the thread.** - First, draw a free-body diagram for the hanging mass. - Then set up \(F = ma\) for the translational motion of the mass. \(T = \_\_\_\_\_\_\_\_\_\_ \, \text{N}.\) **Instructions for Rotational Motion Calculations** 1. **Calculate the torque (τ) on the pulley due to the tension T.** - Formula: τ = __________ Nm 2. **Calculate the angular acceleration (α) of the rotating system.** - Formula: α = __________ rad/s² 3. **Calculate the rotational inertia (I) of the system.** - Formula: I = __________ kg m² 4. **Calculate the contribution to I from the two brass weights.** - **Hint:** I = I_weights + I_rod + I_axle - I_weights = __________ kg m² 5. **Calculate D.** - Formula: D = __________ m These steps outline the process for determining various physical properties of a rotating system, starting with torque and progressing through angular acceleration and rotational inertia calculations, with a focus on contributions from different components.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
Transcribed Image Text:**Part IV. Design Problem – Tuning I: "70 in 7.0 ± 0.7"**
**Objective:**
Your goal is to use your rotating machine to lower a 50-gram mass, starting from rest, through a distance of 70 centimeters in a time of 7.0 ± 0.7 seconds. Use the second-step pulley. The only machine parameter that you can adjust is the location of the brass weights along the rod.
**Schematic:**
The schematic of the rotating machine includes:
- A rod labeled 'L' with brass weights 'M' on either side, where 'D' denotes the adjustable distance from the rotation axis to the center of mass of each brass weight.
- A pulley of radius 'r' connected to a 50-gram mass.
- The setup is centered around the axle rotation axis.
**The Theory:**
To find the value of D, apply theoretical analysis as guided by the questions below:
1. **Calculate the acceleration \(a\) of the hanging mass.**
\(a = \_\_\_\_\_\_\_\_\_\_ \, \text{m/s}^2\).
2. **Calculate the tension \(T\) in the thread.**
- First, draw a free-body diagram for the hanging mass.
- Then set up \(F = ma\) for the translational motion of the mass.
\(T = \_\_\_\_\_\_\_\_\_\_ \, \text{N}.\)
Transcribed Image Text:**Instructions for Rotational Motion Calculations**
1. **Calculate the torque (τ) on the pulley due to the tension T.**
- Formula: τ = __________ Nm
2. **Calculate the angular acceleration (α) of the rotating system.**
- Formula: α = __________ rad/s²
3. **Calculate the rotational inertia (I) of the system.**
- Formula: I = __________ kg m²
4. **Calculate the contribution to I from the two brass weights.**
- **Hint:** I = I_weights + I_rod + I_axle
- I_weights = __________ kg m²
5. **Calculate D.**
- Formula: D = __________ m
These steps outline the process for determining various physical properties of a rotating system, starting with torque and progressing through angular acceleration and rotational inertia calculations, with a focus on contributions from different components.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY