Ask question

Ask question

All categories

4 years ago

5

Two castings are proposed for a study. One casting is a cube 10.16 cm (4 in.) on a side; the other is a rectangle 10.64 cm (16 i

n.) tall × 10.16 cm (4 in.) wide × 2.45 cm (1 in.) thick. Both are cast from the same metal at the same temperature, and the mold material is the same in both cases. If the cube-shaped casting solidifies in 14.5 min, how rapidly do we expect the rectangular casting to solidify?

1 answer:

iren [92.7K]4 years ago

4 0

To solve the problem it is necessary to apply the concepts related to Chvorinov's Law, which states that

$\frac{T_r}{T_c} = (\frac{V_r}{V_c}*\frac{SA_c}{SA_r})^2$

Where,

$V_c$ = Volume cube

$SA_c$ = Superficial Area from Cube

$V_r$ = Volume Rectangle

$SA_r$ = Superficial Area from Rectangle

Our values are given as (I will try to develop the problem in English units for ease of calculations),

$V_c = 4^3 = 64in^3$

$SA_c = 6*4^2=96in^2$

$SA_r = 2*(1*16+4*1+16*4)=168in^2$

$V_r = 4*1*16 = 64in^3$

Applying the Chvorinov equation we have to,

$\frac{T_r}{T_c} = (\frac{V_r}{V_c}*\frac{SA_c}{SA_r})^2$

$\frac{T_r}{T_c} = (\frac{64}{64}*\frac{96}{168})^2$

$\frac{T_r}{T_c} = (\frac{96}{168})^2$

$\frac{T_r}{T_c} = 0.3265$

The stipulated time for the cube is 14.5 then,

$T_r = 0.3265*14.5$

$T_r = 4.735min$

You might be interested in

The critical angle of diamond is 24 degrees. What is its refractive index?

jolli1 [7]

Answer:

2.46

Explanation:

From the question given above, the following data were obtained:

Critical angle (C) = 24 °

Refractive index (n) =?

The refractive index of the diamond can be obtained by using the following formula as illustrated below:

Refractive index (n) = 1 / sine [critical angle (C)]

n = 1/sine C

n = 1 / sine 24 °

n = 1/0.4067

n = 2.46

Thus, the refractive index of the diamond is 2.46

3 0

3 years ago

A man steps off a diving platform lands in the water below. If he were to miss the water and land on the concrete, his change in

kari74 [83]

Answer:

if he were to land on concrete, he would most likely die and stop all momentum and for the water, he'd most likely live/die (mostly live) and slow momentum to a stop and rise up to the surface

Explanation:

that's the explanation now i gotta execute order 66

7 0

3 years ago

Your friend's 10.8 g graduation tassel hangs on a string from his rearview mirror. When he accelerates from a stoplight, the tas

Nitella [24]

The tension in the string holding the tassel and the vertical will the tension in the string

T = 0.1953 N
Ф = 34.4 °

<h3>What is the tension in the string holding the tassel. ?</h3>

Generally, the equation for Tension is mathematically given as

$TCos\theta = mg$

Therefore

$TCos6.58^{o} = 19.8*10^{-3}*9.8$

T = 0.1953 N

b).

Where

$T* sin \theta = ma$

$0.1953*Sin6.58 \textdegree = 19.8*10^{-3}*a$

a = 1.13 m/s^2

In conclusion

T* sinФ = ma

2msinФ = ma

2sinФ = a

$sin\theta = \frac{a}{2}$

$\theta = sin^{-1}\frac{a}{2} \\\\\theta= sin^{-1}\frac{1.13}{2}$

Ф = 34.4 °

In conclusion, The tension in the string holding the tassel and the vertical will the tension in the string

T = 0.1953 N

Ф = 34.4 °

Read more about tension

brainly.com/question/15880959

#SPJ1

4 0

2 years ago

Your teacher had not exercised since the beginning of distance learning. She decided to exercise by walking in the park. The par

Lesechka [4]

A) 6000 m

B) 0 m

C) 3.33 m/s

D) 0 m/s

Explanation:

a)

In physics, distance is a scalar quantity that represents the total length of the path covered by an object during its motion.

Being a scalar quantity, it has no direction, but only a magnitude (so, a number + its units).

The distance covered by a body can be calculated by adding together all the lengths of all the motion of the body.

In this problem, the teacher walks in the partk, starting at position A, then walking around the park 5 times and returning to the original position.

The park has a rectangular shape 200 m x 400 m, so the perimeter of the park is:

$p=200+400+200+400=1200 m$

The teacher covers the perimeter 5 times, so the total distance she covered is:

$d=5p=5\cdot 1200 =6000 m$

B)

Displacement, instead, is a vector quantity that connects the initial position to the final position of the motion of an object.

Being a vector, it has both a magnitude and a direction, where:

- The magnitude is equal to the length of the vector, so it corresponds to the shortest distance in a straight line between the initial and final position

- The direction goes from the initial position to the final position

In this problem:

- The teacher starts her motion at position A

- The teacher ends her motion at position A

So, the distance between the initial and final position is zero:

$d=x_A -x_A = 0$

And therefore, the displacement is zero.

C)

The average speed of an object is a scalar quantity telling us how fast an object is moving, regardless of its direction of motion.

Being a scalar quantity, it has only a magnitude, and no direction.

The average speed is given by the equation:

$v=\frac{d}{t}$

where

d is the distance covered by the object

t is the time elapsed

In this problem we have:

d = 6000 m is the distance covered by the teacher

t = 30 min = 1800 s is the time elapsed

Therefore, the average speed is:

$v=\frac{6000}{1800}=3.33 m/s$

D)

The average velocity of an object is a vector quantity telling us how fast an object is moving but also its direction of motion.

Being a vector, it has both a magnitude and a direction, where:

- The direction corresponds to the direction of the displacement

- The magnitude is given by the formula:

$v=\frac{d}{t}$

where

d is the displacement of the object

t is the time elapsed

In this problem:

d = 0 is the displacement of the teacher

t = 1800 s is the time elapsed

Therefore, the average velocity is zero:

$v=\frac{0}{1800}=0 m/s$

7 0

3 years ago

When do you produce more pressure on the ground...standing or laying down?

ycow [4]

When you are Standing you produce more pressure on the ground

7 0

3 years ago