Question

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

Answer 1

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.

Answer 2

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

Further explanation

Acceleration is rate of change of velocity.

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

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

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem!

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.

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

The minimum speed that the conveyor must move:

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

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

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

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

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

Learn more

• 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

Answer details

Grade: High School

Subject: Physics

Chapter: Kinematics

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