## Problem Statement### Scenario:On a very rainy day, Nick drags a box of old books to the bookstore to sell. The box moves through the puddles at a velocity of $ U = 10 \, \text{ft/min} $. For all calculations, use an approximation that the box follows the given dimensions.### Task:1. **Calculate the force required to keep the box moving at $ U $.** - **Hints:** Obtain the drag coefficient by calculating the Reynolds number. Consider the projected area as the bottom plus the two long sides.2. **Determine the power (in watts) required to overcome the skin friction drag.**### Diagram:The diagram shows a rectangular box with the following dimensions:- Length ($ L $) = 3 feet- Breadth ($ B $) = 2 feet- Depth ($ D $) = 2 inches (converted to feet: $ \frac{2}{12} = \frac{1}{6} \, \text{ft} $)The box is submerged partially in water, up to a "water line" shown on the sides, with velocity $ U $ indicated as the direction of motion.### Considerations for Calculations:- The projected area to take into account includes the bottom area and two side areas submerged in water.- Use appropriate formulas to calculate the Reynolds number to determine the drag coefficient.- Use physics principles to determine the force and power needed.

Given,the velocity of the box, length of the box, the breadth of the box, depth of the box, let the…

Answered: 3. On a very rainy day, Nick drags a…

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## Problem Statement

### Scenario:
On a very rainy day, Nick drags a box of old books to the bookstore to sell. The box moves through the puddles at a velocity of $ U = 10 \, \text{ft/min} $. For all calculations, use an approximation that the box follows the given dimensions.

### Task:
1. **Calculate the force required to keep the box moving at $ U $.**
- **Hints:** Obtain the drag coefficient by calculating the Reynolds number. Consider the projected area as the bottom plus the two long sides.

2. **Determine the power (in watts) required to overcome the skin friction drag.**

### Diagram:
The diagram shows a rectangular box with the following dimensions:
- Length ($ L $) = 3 feet
- Breadth ($ B $) = 2 feet
- Depth ($ D $) = 2 inches (converted to feet: $ \frac{2}{12} = \frac{1}{6} \, \text{ft} $)

The box is submerged partially in water, up to a "water line" shown on the sides, with velocity $ U $ indicated as the direction of motion.

### Considerations for Calculations:
- The projected area to take into account includes the bottom area and two side areas submerged in water.
- Use appropriate formulas to calculate the Reynolds number to determine the drag coefficient.
- Use physics principles to determine the force and power needed.

Expert Solution

Step 1: Drag force

Given,

the velocity of the box,

$U equals 10 space f t divided by m i n U equals 10 cross times 0.00508 space m divided by s U equals 0.0508 m divided by s$

length of the box,

$L equals 3 space f t L equals 3 cross times 0.3048 m L equals 0.9144 m$

the breadth of the box,

$B equals 2 space f t B equals 2 cross times 0.3048 m B equals 0.6096 m$

depth of the box,

$D equals 2 f t D equals 2 cross times 0.3048 m D equals 0.6096 m$

let the normal drag coefficient be $C subscript D equals 0.2$

The required force,

$F subscript D equals C subscript D A rho subscript w U squared over 2 F subscript D equals 0.2 cross times open parentheses L cross times B close parentheses cross times 1000 cross times fraction numerator 0.0508 squared over denominator 2 end fraction F subscript D equals 0.2581 cross times open parentheses 0.9144 cross times 0.6096 close parentheses F subscript D equals 0.144 space N$

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