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2 years ago

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At the metal-casting company where you work, you must set up a conveyor system to move castings from the furnace to the heat tre

atment area 55 yards away. The castings cool at the rate of 0.3°F (degrees Fahrenheit) per second and must not be allowed to cool more than 7°F before being heat treated. What is the minimum speed, in feet per second, that the conveyor must move?

2 answers:

Mazyrski [523]2 years ago

5 0

Answer:

2.35 yards/second or 7.07 ft/second

Step-by-step explanation:

The distance to be covered is 55 yards.

The casting cools at the rate of $0.3^\circ \text F$ and the temperature must not be allowed to cool more than $7^\circ \text F$ .

We know that, $\text {distance} = \frac{\text {speed}}{\text {time}}$

By the time, the temperature reaches $7^\circ \text F$ , it will take about,

$\frac{7}{0.3}=23.33\text s$ , so it will take about 23.33 seconds.

Also, 55 yards = $55 \times 3 =165 ft$

So the minimum speed that conveyor must move is,

$\frac{165}{23.33}=7.07 ft/s$

Hence, the speed of conveyor is 7.07 feet per second.

Marat540 [252]2 years ago

5 0

The minimum speed that the conveyor must move is about 7 ¹/₄ feet/second

<h3>Further explanation</h3>

Acceleration is rate of change of velocity.

$\large {\boxed {a = \frac{v - u}{t} } }$

$\large {\boxed {d = \frac{v + u}{2}~t } }$

<em>a = acceleration ( m/s² )</em>

<em>v = final velocity ( m/s )</em>

<em>u = initial velocity ( m/s )</em>

<em>t = time taken ( s )</em>

<em>d = distance ( m )</em>

Let us now tackle the problem!

<em>The castings cool at the rate of 0.3 °F per second and must not be allowed to cool more than 7°F before being heat treated.</em>

$\texttt{Maximum Time Allowed} = 7 \div 0.3 = \frac{70}{3} \texttt{ seconds}$

<em>The minimum speed that the conveyor must move:</em>

$\texttt{Minimum Speed} = \texttt{Distance} \div \texttt{Maximum Time Allowed}$

$\texttt{Minimum Speed} = 55 \div \frac{70}{3}$

$\texttt{Minimum Speed} = 2\frac{5}{14} \texttt{ yards/second}$

$\texttt{Minimum Speed} = 2\frac{5}{14} \times 3 \texttt{ feet/second}$

$\texttt{Minimum Speed} = 7\frac{1}{14} \texttt{ feet/second}$

<h3>Learn more</h3>

Velocity of Runner : brainly.com/question/3813437
Kinetic Energy : brainly.com/question/692781
Acceleration : brainly.com/question/2283922
The Speed of Car : brainly.com/question/568302

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Conveyor , Speed

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