Marble A is placed in a hollow tube, and the tube is swung in a horizontal plane causing the marble to be thrown out. As viewed

Response:

1) g=31.87ft/s^2

2)m=120

W=119.64lbf

Clarification:

initial segment

the weight of an object with a specified mass is determined using the equation

W=mg

we need to convert 120lb into slug

m=120lbx1slug/32.147lb=3.733slug

calculating for g

g=W/m

g=119/3.733=31.87ft/s^2

subsequent segment

the mass remains unchanged

m=120lb=3.733slug

Weight

W=3.733slug*32.05ft/s^2=119.64lbf

Answer:

90 L.atm

Explanation:

According to the provided details:

First pathway:

A( 3 atm, 20 L) → C ( 1 atm, 20 L) → D (1 atm, 50 L)

Second pathway:

A(3 atm, 20 L) → B( 3 atm, 50 L) → D ( 1 atm, 50 L)

As the number of moles is 1.00 moles

To calculate wAB;

A → B signifies the transformation is happening at a steady pressure;

Thus,

wAB = pressure multiplied by the change in volume

wAB = P(V₂ - V₁)

wAB = 3 atm (50 L - 20 L)

wAB = 3 atm (30 L)

wAB = 90 L.atm

Response:

The confidence scale is an ordinal measurement scale

Clarification:

An ordinal measurement scale is utilized for assessing attributes that can be ranked or ordered, yet the intervals in between attributes lack quantitative meaning. In this scenario, the scale utilized was from 1 to 7, where "1" signifies that the defendant's race has little impact on jury verdicts, and "7" indicates a strong impact of race on such verdicts. For instance, in a survey measuring customer satisfaction for a product, a "1" indicates great dissatisfaction, while "10 " denotes highest satisfaction. In the first instance, it would be incorrect to assert that the difference between a rating of 1, which implies "not at all," and perhaps a 3, is equivalent to the gap between a 5 and a 7, as these numbers merely serve as labels devoid of quantifiable value.

Other types of measurement levels include:

1. Nominal: This is the most straightforward measurement level, employed primarily for categorizing attributes. An example would be gathering data on gender, with categories such as male, female, and transgender.

2. Interval: An interval scale is used when the distances between two attributes hold meaning, but a true zero point is absent from the scale.

3. Ratio: This level combines all three previously mentioned measurements, serving to categorize, show ranking, maintain meaningful distances between attributes, and possess a true zero point. A typical example is measuring temperature using a Celsius thermometer, which has a true zero at 0°C, and the intervals between 5°C and 10°C are equivalent to those between 10°C and 15°C.

Answer:

Time constant = 15.34 seconds

The thermometer indicates an error margin of 0.838°

Explanation:

Given

t = 1 minute = 60 seconds

c(t) = 98% = 0.98

According to the details provided, the thermometer functions as a first-order system.

The transfer function of such a system is expressed as;

C(s)/R(s) = 1/(sT + 1).

To determine the time constant, the step response must be evaluated.

This is defined as

r(t) = u(t) --- Applying Laplace Transformation

R(s) = 1/s

Replacing 1/s back into C(s)/R(s) = 1/(sT + 1).

What we have

C(s)/1/s = 1/(sT + 1)

C(s) = 1/(sT + 1) * 1/s

C(s) = 1/s - 1/(s + 1/T) --- Taking Inverse Laplace Transformation

L^-1(C(s)) = L^-1(1/s - 1/(s + 1/T))

Given that e^-t <–> 1/(s + 1) --- {L}

1 <–> 1/s {L}

Thus, the unit response c(t) = 1 - e^-(t/T)

Substituting 0.98 for c(t) and 60 for t

0.98 = 1 - e^-(60/T)

0.98 - 1 = - e^-(60/T)

-0.02 = - e^-(60/T)

e^-(60/T) = 0.02

ln(e^-(60/T)) = ln(0.02)

-60/T = -3.912

T = -60/-3.912

T = 15.34 seconds

It follows that the time constant = 15.34 seconds

The error signal is characterized by

E(s) = R(s) - C(s)

Where the temperature shifts at 10°/min; which equals 10°/60 s = 1/6

Thus,

E(s) = R(s) - 1/6 C(s)

Calculating C(s)

C(s) = 1/s - 1/(s + 1/T)

C(s) = 1/s - 1/(s + 1/15.34)

Note that R(s) = 1/s

Thus, E(s) turns into

E(s) = 1/s - 1/6(1/s - 1/(s + 1/15.34))

E(s) = 1/s - 1/6(1/s - 1/(s + 0.0652)

E(s) = 1/s - 1/6s + 1/(6(s+0.0652))

E(s) = 5/6s + 1/(6(s+0.0652))

E(s) = 0.833/s + 1/(6(s+0.0652)) ---- Taking Inverse Laplace Transformation

e(t) = 1/6e^-0.652t + 0.833

In a first-order system, a steady state condition is reached when the time is four times the time constant.

Thus,

Time = 4 * 15.34

Time = 61.36 seconds

Consequently, e(t) becomes

e(t) = 1/6e^-0.652t + 0.833

e(t) = 1/(6e^-0.652(61.36)) + 0.833

e(t) = 0.83821342824942664566211

e(t) = 0.838 --- Rounded off

Thus, the thermometer reveals an error of 0.838°