1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dangina [55]
2 years ago
12

A 3-phase induction motor with 4 poles is being driven at 45 Hz and is running in its normal operating range. When connected to

a certain load, the motor rotates at a speed of 1070 rpm and outputs 800W a. What is the slip and developed torque? b. What is the new slip and motor speed if the developed torque is reduced to 4 Nm?
Engineering
1 answer:
Dennis_Churaev [7]2 years ago
5 0

Answer:

a) The slip for the given conditions is 0.2074 or 20.74% and the developed torque is 7.14 Nm.

b) The new slip after reducing the torque to 4 Nm is 0.1162 or 11.62% and the new motor speed is 1193.13 rpm.

Explanation:

In order to find the slip we can use the definition as the relative difference between Synchronous speed and the rotor speed and that the developed torque is the ratio between output power and rotor angular velocity.

Slip.

We can find the synchronous speed u sing the following formula

N_s =\cfrac{120f}p

Where f stands for the frequency and p the number of poles, so we have

N_s = \cfrac{120(45)}{4}\\N_s =1350 \,rpm

Replacing on the slip formula

S = \cfrac{N_s-N_r}{N_s}

we get

S = \cfrac{1350-1070}{1350}\\ S = 0.2074

Thus the slip for the given conditions is 0.2074 or 20.74%.

Developed torque.

We can find the angular velocity in radians per second

\omega_r =1070  \cfrac{rev}{min} \times \cfrac{1 \, min}{60 \, s}\times \cfrac{2\pi rad}{1 \, rev}\\\omega_r =112.05 \, \cfrac{rad}{s}

Thus we can replace on the torque formula

\tau = \cfrac{P}{\omega_r}\\\tau=\cfrac{800 W}{112.05 \, \cfrac{rad}{s}}

We get

\tau = 7.14\,  N m

The developed torque is 7.14 Nm.

Slip for the reduced torque.

The torque is proportional to the slip, so we can write

\cfrac{\tau_1}{\tau_2}= \cfrac{S_1}{S_2}

Thus solving for the new slip S_2 we have:

S_2 = S_1 \cfrac{\tau_2}{\tau_1}

Replacing the values obtained on the previous part we have

S_2 = 0.2074 \cfrac{4 Nm}{7.14 Nm}\\ S_2=0.1162

So the new slip after reducing the torque to 4 Nm is 0.1162 or 11.62%

Motor speed.

We can use the slip definition

S_2 =\cfrac{N_s-N_{r_2}}{N_s}

Solving for the motor speed we have

S_2N_s =N_s-N_{r_2}

N_{r_2}=N_s-S_2N_s \\N_{r_2}=N_s(1-S_2)

Replacing values we have

N_{r_2}=1350 \, rpm(1-0.1162)\\N_{r_2}=1193.13 rpm

The new motor speed is 1193.13 rpm.

You might be interested in
A light bar AD is suspended from a cable BE and supports a 20-kg block at C. The ends A and D of the bar are in contact with fri
babymother [125]

Answer:

Tension in cable BE= 196.2 N

Reactions A and D both are  73.575 N

Explanation:

The free body diagram is as attached sketch. At equilibrium, sum of forces along y axis will be 0 hence

T_{BE}-W=0 hence

T_{BE}=W=20*9.81=196.2 N

Therefore, tension in the cable, T_{BE}=196.2 N

Taking moments about point A, with clockwise moments as positive while anticlockwise moments as negative then

196.2\times 0.125- 196.2\times 0.2+ D_x\times 0.2=0

24.525-39.24+0.2D_x=0

D_x=73.575 N

Similarly,

A_x-D_y=0

A_x=73.575 N

Therefore, both reactions at A and D are 73.575 N

7 0
3 years ago
. En la facultad de Ingeniería Industrial se realizó una encuesta a 200 personas para saber que lenguaje de programación preferí
GarryVolchara [31]

Answer:

lalalalapumpe

Explanation:

4 0
3 years ago
Jordan's dad made a new recipe for dinner. Jordan looked at the food and saw that it was white, yellow, and purple in color. She
zhenek [66]

Answer:

Jordan used her eyes to see the food, her touch to feel the food, and her nose to smell the food, and lastly, but most importantly, she used her mouth to taste the food.

7 0
2 years ago
Saturated liquid water flows through 2 cm ID stainless steel tubes at 200 g/s. The water is at 80oC and the inside surface of th
EleoNora [17]

Answer:

steel

Explanation:

8 0
2 years ago
Hareem and Shahad are on a road trip to Florida. They pull over to get gas, and as you may know it is sold by the gallon in the
Alona [7]

Answer:

53.3

Explanation:

4×14=56

56÷1.05=53.3

4 0
3 years ago
Other questions:
  • A pipe of 10 cm inner diameter is used to send crude oil over distance of 400 meters. The entire pipe was laid horizontal. The v
    5·1 answer
  • A three-phase voltage source with a terminal voltage of 22kV is connected to a three-phase transformer rated 5MVA 22kV/220V. The
    8·1 answer
  • Find the inductive reactance per mile of a single-phase overhead transmission line operating at 60 Hz, given the conductors to b
    6·1 answer
  • The flow curve for a certain metal has parameters: strain-hardening
    8·1 answer
  • A completely reversible heat pump produces heat ata rate of 300 kW to warm a house maintained at 24°C. Theexterior air, which is
    6·1 answer
  • Pls help! 39 points!!
    5·2 answers
  • Introduction to gear and gear ratios: If you have two gears of the same size does the output speed increase, decrease, or remain
    13·1 answer
  • Do all websites use the same coding to create?
    8·1 answer
  • If fog is so bad that I can’t see for short distance what should I do
    9·2 answers
  • If a fuel line is routed through a compartment parallel with an electrical wire bundle, the fuel line should be installed ______
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!