4) Calculations for the red dog food can rolling down the slope in the Rube Goldberg design are as follows (we will name it Step 1): Step 1 (calculations are given): Coefficient of friction → μ = 0.14 Mass of the object →m-368 gm -0.368kg Initial height of the object (red can on top of books)→ h-8.89, cm -0.0889 m Slope of the file folder → 9-14° Travelling Distance by the object = 11.5 inch = 0.292 m And length that the object will travel-h/sin 8-0.0889/ sin14° = 0.367 m So, the radius of the object-R-0.367 -0.292 -0.075 m Initial Velocity of red can → u=0 Velocity and Force Calculations for Step 1: -From total mechanical energy conservation: →→Initial mechanical energy = final mechanical energy- mg - In case of pure rolling, the velocity of the center of mass: → V-Ro-0.075 x 14.28 1.07 m/s. -Hence the change in force acting on the object for the travel: →F-mgsinė 0.368 × 9.81 x sin14° -0.89 N Step 2: The Selective Step (Step 2) in this design and for the questions below involves the white dog food can at the bottom of the slope that is hit by the red dog food can. A. Equations for Step 2: Provide the equations that can be used to describe the change in type and amount of energy across Step 2.
4) Calculations for the red dog food can rolling down the slope in the Rube Goldberg design are as follows (we will name it Step 1): Step 1 (calculations are given): Coefficient of friction → μ = 0.14 Mass of the object →m-368 gm -0.368kg Initial height of the object (red can on top of books)→ h-8.89, cm -0.0889 m Slope of the file folder → 9-14° Travelling Distance by the object = 11.5 inch = 0.292 m And length that the object will travel-h/sin 8-0.0889/ sin14° = 0.367 m So, the radius of the object-R-0.367 -0.292 -0.075 m Initial Velocity of red can → u=0 Velocity and Force Calculations for Step 1: -From total mechanical energy conservation: →→Initial mechanical energy = final mechanical energy- mg - In case of pure rolling, the velocity of the center of mass: → V-Ro-0.075 x 14.28 1.07 m/s. -Hence the change in force acting on the object for the travel: →F-mgsinė 0.368 × 9.81 x sin14° -0.89 N Step 2: The Selective Step (Step 2) in this design and for the questions below involves the white dog food can at the bottom of the slope that is hit by the red dog food can. A. Equations for Step 2: Provide the equations that can be used to describe the change in type and amount of energy across Step 2.
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
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Transcribed Image Text:### Step 1: Calculations for the Red Dog Food Can Rolling Down the Slope
In this educational section, we will perform calculations for a red dog food can rolling down a slope as part of a Rube Goldberg design.
#### Step 1 (Calculations Provided):
1. **Coefficient of Friction (μ):** 0.14
2. **Mass of the Object (m):** 368 gm = 0.368 kg
3. **Initial Height of the Object (h):** 8.89 cm = 0.0889 m
4. **Slope of the File Folder (θ):** 14°
5. **Traveling Distance by the Object:**
- 11.5 inches = 0.292 m
6. **Length that the Object will Travel:**
- \( \frac{h}{\sin{\theta}} = \frac{0.0889}{\sin{14°}} = 0.367 \, \text{m} \)
7. **Radius of the Object (R):**
- \( R = 0.367 - 0.292 = 0.075 \, \text{m} \)
8. **Initial Velocity of Red Can (u):** 0
#### Velocity and Force Calculations for Step 1:
Using the principle of mechanical energy conservation:
- **Initial Mechanical Energy = Final Mechanical Energy**
- **Potential Energy (Initial) = Kinetic Energy (Final) + Work Done Against Friction**
- In the case of pure rolling, the velocity (V) of the center of mass:
- \( V = R \omega = 0.075 \times 14.28 = 1.07 \, \text{m/s} \)
- The change in force acting on the object for travel:
- \( F = mg \sin{\theta} = 0.368 \times 9.81 \times \sin{14°} = 0.89 \, \text{N} \)
### Step 2: The Selective Step (Step 2)
This step in the design and the next calculations involve the white dog food can positioned at the bottom of the slope. It is struck by the red dog food can.
#### A. Equations for Step 2:
Provide the equations necessary to describe the change in type and amount of energy across Step 2.
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