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neonofarm [45]
2 years ago
11

An electric motor M is used to reel in cable and hoist a bicycle into the ceiling space of a garage. Pulleys are fastened to the

bicycle frame with hooks at location:s A and B, and the motor can reel in cable at a steady rate of 12 in./sec. At this rate, how long will it take to hoist the bicycle 5 feet into the air? Assume that the bicycle remains level.
Engineering
1 answer:
Fantom [35]2 years ago
3 0

Answer:

<em>time taken = 5 sec </em>

<em></em>

Explanation:

Rate at which motor can reel bicycle = 12 in/sec

height to hoist the bicycle by = 5 ft

time that will be taken to get to this height = ?

first we convert the height required to inches.

<em>12 inches = 1 ft</em>, therefore,

5 ft = (5 x 12) inches = 60 inches

Time that will be taken to get to this height assuming the remains level will be,

<em>time = height/rate of reeling</em>

time = 60/12 = <em>5 sec</em>

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The purification of hydrogen gas is possible by diffusion through a thin palladium sheet. Calculate the number of kilograms of h
diamong [38]

Answer:

M=0.0411 kg/h or 4.1*10^{-2} kg/h

Explanation:

We have to combine the following formula to find the mass yield:

M=JAt

M=-DAt(ΔC/Δx)

The diffusion coefficient : D=6.0*10^{-8} m/s^{2}

The area : A=0.25 m^{2}

Time : t=3600 s/h

ΔC: (0.64-3.0)kg/m^{3}

Δx: 3.1*10^{-3}m

Now substitute the  values

M=-DAt(ΔC/Δx)

M=-(6.0*10^{-8} m/s^{2})(0.25 m^{2})(3600 s/h)[(0.64-3.0kg/m^{3})(3.1*10^{-3}m)]

M=0.0411 kg/h or 4.1*10^{-2} kg/h

8 0
2 years ago
A converging-diverging nozzle is designed to operate with an exit Mach number of 1.75 . The nozzle is supplied from an air reser
Flura [38]

Answer:

a. 4.279 MPa

b. 3.198 MPa to 4.279 MPa

c. 0.939 MPa

d. Below 3.198 MPa

Explanation:

From the given parameters

M_{exit} = 1.75 MPa  

M at 1.6 MPa gives A_{exit}/A* = 1.2502

M at 1.8 MPa gives  A_{exit}/A* = 1.4390

Therefore, by interpolation, we have M_{exit} = 1.75 MPa  gives A

However, we shall use M_{exit} = 1.75 MPa and A

Similarly,

P_{exit}/P₀ = 0.1878

a) Where the nozzle is choked at the throat there is subsonic flow in the following diverging part of the nozzle. From tables, we have

A_{exit}/A* = 1.387. by interpolation M

Therefore P_{exit} = P₀ × P

Which shows that the nozzle is choked for back pressures lower than 4.279 MPa

b) Where there is a normal shock at the exit of the nozzle, we have;

M₁ = 1.75 MPa, P₁ = 0.1878 × 5 = 0.939 MPa

Where the normal shock is at M₁ = 1.75 MPa, P₂/P₁ = 3.406

Where the normal shock occurs at the nozzle exit, we have

P_b = 3.406\times 0.939 = 3.198 MPa

Where the shock occurs t the section prior to the nozzle exit from the throat, the back pressure was derived as P_b = 4.279 MPa

Therefore the back pressure value ranges from 3.198 MPa to 4.279 MPa

c) At M_{exit} = 1.75 MPa  and P

d) Where the back pressure is less than 3.198 MPa according to isentropic flow relations supersonic flow will exist at the exit plane    

8 0
2 years ago
An automobile having a mass of 900 kg initially moves along a level highway at 100 km/h relative to the highway. It then climbs
creativ13 [48]

Answer:

ΔKE=-347.278 kJ

ΔPE= 441.45 kJ

Explanation:

given:

mass m=900 kg

the gravitational acceleration g=9.81 m/s^2

the initial velocity V_{1}=100 km/h-->100*10^3/3600=27.78 m/s

height above the highway h=50 m

h1=0m

the final velocity V_{F}=0 m/s

<u>To find:</u>

the change in kinetic energy ΔKE

the change in potential energy ΔPE

<u>assumption:</u>

We take the highway as a datum

<u>solution:</u>

ΔKE=5*m*(V_{F}^2-V_{1}^2)

      =-347.278 kJ

ΔPE=m*g*(h-h1)

      = 441.45 kJ

5 0
2 years ago
A thermometer requires 1 minute to indicate 98% of the response to a unit step input. Assuming the thermometer to be a first ord
Rama09 [41]

Answer:

Time constant = 15.34 seconds

The thermometer shows an error of 0.838°

Explanation:

Given

t = 1 minute = 60 seconds

c(t) = 98% = 0.98

According to the question, the thermometer is a first order system.

The first order system transfer function is given as;

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

To calculate the time constant, we need to calculate the step response.

This is given as

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

R(s) = 1/s

Substitute 1/s for R(s) in C(s)/R(s) = 1/(sT + 1).

We have

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

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

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

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

Since, e^-t <–> 1/(s + 1) --- {L}

1 <–> 1/s {L}

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

Substitute 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

Time constant = 15.34 seconds

The error signal is given as

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

Where the temperature changes at the rate of 10°/min; 10°/60 s = 1/6

So.

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)

Remember that R(s) = 1/s

So, E(s) becomes

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)) ---- Take Inverse Laplace Transformation

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

For a first order system, the system attains a steady state condition when time is 4 times of Time constant.

So,

Time = 4 * 15.34

Time = 61.36 seconds

So, 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 --- Approximated

Hence, the thermometer shows an error of 0.838°

4 0
2 years ago
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True or False:A retractable service pit cover can help other shop employees from falling into the pit while another technician i
coldgirl [10]

Answer:

f

Explanation:

7 0
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